The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 16 19:46 EDT 2021. Contains 343951 sequences. (Running on oeis4.)