The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A136446 Numbers n such that some subset of the numbers { 1 < d < n : d divides n } adds up to n. 9
 12, 18, 24, 30, 36, 40, 42, 48, 54, 56, 60, 66, 72, 78, 80, 84, 90, 96, 100, 102, 108, 112, 114, 120, 126, 132, 138, 140, 144, 150, 156, 160, 162, 168, 174, 176, 180, 186, 192, 196, 198, 200, 204, 208, 210, 216, 220, 222, 224, 228, 234, 240, 246 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This is a subset of the pseudoperfect numbers A005835 and thus non-deficient (A023196), but in view of the definition actually abundant numbers (A005101). Sequence A122036 lists odd abundant numbers (A005231) which are not in this sequence. So far, 351351 is the only one we know. (As of today, no odd weird (A006037: abundant but not pseudoperfect) number is known.) - M. F. Hasler, Apr 13 2008 This sequence contains infinitely many odd elements: any proper multiple of any pseudoperfect number is in the sequence, so odd proper multiples of odd pseudoperfect numbers are in the sequence. The first such is 2835 = 3 * 945 (which is in the b-file). - Franklin T. Adams-Watters, Jun 18 2009 A211111(a(n)) > 1. - Reinhard Zumkeller, Apr 04 2012 REFERENCES Mladen Vassilev, Two theorems concerning divisors, Bull. Number Theory Related Topics 12 (1988), pp. 10-19. LINKS M. F. Hasler, Table of n, a(n) for n = 1..24491 (confirmed by R. J. Mathar, Mar 20 2011). MAPLE isA136446a := proc(s, n) if n in s then return true; elif add(i, i=s) < n then return false; elif nops(s) = 1 then is(op(1, s)=n) ; else sl := sort(convert(s, list), `>`) ; for i from 1 to nops(sl) do m := op(i, sl) ; if n -m = 0 then return true; end if ; if n-m > 0 then sr := [op(i+1..nops(sl), sl)] ; if procname(convert(sr, set), n-m) then return true; end if; end if; end do; return false; end if; end proc: isA136446 := proc(n) isA136446a( numtheory[divisors](n) minus {1, n}, n) ; end proc: for n from 1 to 400 do if isA136446(n) then printf("%d, ", n) ; end if; end do ; # R. J. Mathar, Mar 20 2011 MATHEMATICA okQ[n_] := Module[{d}, If[PrimeQ[n], False, d = Most[Rest[Divisors[n]]]; MemberQ[Plus @@@ Subsets[d], n]]]; Select[Range[2, 246], okQ] (* T. D. Noe, Jul 24 2012 *) PROG (PARI) N=72 \\ up to this value vv=vector(N); { for(n=2, N, if ( isprime(n), next() ); d=divisors(n); d=vector(#d-2, j, d[j+1]); \\ not n, not 1 for (k=1, (1<<#d)-1, \\ all subsets t=vecextract(d, k); if ( n==sum(j=1, #t, t[j]), vv[n] += 1; ); ); ); } for (j=1, #vv, if (vv[j]>0, print1(j, ", "))) \\ A005835 (after correction) (PARI) is_A136446(n, d=divisors(n))={#d>2 && is_A005835(n, d[2..-2])} \\ Replaced old code not conforming to current PARI syntax. - M. F. Hasler, Jul 28 2016 for( n=1, 10^4, is_A136446(n) && print1(n", ")) \\ M. F. Hasler, Apr 13 2008 (Haskell) a136446 n = a136446_list !! (n-1) a136446_list = map (+ 1) \$ findIndices (> 1) a211111_list -- Reinhard Zumkeller, Apr 04 2012 (Sage) def isa(s, n): # After R. J. Mathar's Maple code if n in s: return True if sum(s) < n: return False if len(s) == 1: return s[0] == n for i in srange(len(s)-1, -1, -1) : d = n - s[i] if d == 0: return True if d > 0: if isa(s[i+1:], d): return True return False isA136446 = lambda n : isa(divisors(n)[1:-1], n) [n for n in (1..246) if isA136446(n)] # Peter Luschny, Jul 23 2012 CROSSREFS See A005835 (allowing for divisor 1). Cf. A122036 = A005231 \ A136446. Sequence in context: A297925 A341099 A175837 * A074726 A341475 A091013 Adjacent sequences: A136443 A136444 A136445 * A136447 A136448 A136449 KEYWORD nonn AUTHOR Joerg Arndt, Apr 06 2008 EXTENSIONS More terms from M. F. Hasler, Apr 13 2008 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 10 02:09 EST 2022. Contains 358712 sequences. (Running on oeis4.)