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!)
 A125225 Numbers n such that n-1 can be represented as a sum of a subset of divisors of n. 2
 1, 2, 4, 6, 8, 12, 16, 18, 20, 24, 28, 30, 32, 36, 40, 42, 48, 54, 56, 60, 64, 66, 70, 72, 78, 80, 84, 88, 90, 96, 100, 104, 108, 112, 120, 126, 128, 132, 140, 144, 150, 156, 160, 162, 168, 176, 180, 192, 196, 198, 200, 204, 208, 210, 216, 220, 224, 228, 234, 240, 252 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The definition is related to that for semiperfect numbers (A005835). Every practical number (A005153) belongs to this sequence but not necessarily vice versa; e.g., 70 is in this sequence but not practical. Every number n in this sequence has sigma(n) >= 2n-1 (A103288) but, despite being abundant, 102 is not in this sequence. Such numbers can be used to construct inheritance puzzles of the type described by Premchand Anne (see link). Does the sequence contain A005231 (the odd abundant numbers)? - Robert Israel, Aug 05 2016 LINKS T. D. Noe, Table of n, a(n) for n=1..1000 Premchand Anne, Egyptian fractions and the inheritance problem, The College Mathematics Journal 29 (4) (1998) 296-300. EXAMPLE 70 is in this sequence because 70-1=69=35+14+10+7+2+1 and all numbers in the sum are divisors of 70. MAPLE ss:= proc(n, S) local s, Sp;  option remember;   if n = 0 then return true   elif S = {} then return false   fi;   s:= max(S);   if s > n then return procname(n, select(`<=`, S, n))   elif s = n then return true   fi;   s:= min(S);   Sp:= subs(s=NULL, S);   if s > n then false   else procname(n-s, Sp) or procname(n, Sp)   fi end proc: select(n -> ss(n-1, numtheory:-divisors(n)), [\$1..1000]); # Robert Israel, Aug 05 2016 MATHEMATICA okQ[n_] := With[{dd = Divisors[n]}, AnyTrue[Range[Length[dd], 1, -1], AnyTrue[Subsets[dd, {#}], Total[#] == n-1&]&]]; okQ[1] = True; Select[Range[1000], okQ] (* Jean-François Alcover, Jul 23 2020 *) PROG (PARI) padbin(n, len) = {b = binary(n); while(length(b) < len, b = concat(0, b); ); b; } isok(n) = {if (n == 1, return (1)); d = divisors(n); nbd = #d; for (i = 1, 2^nbd-1, b = padbin(i, nbd); s = sum(j = 1, nbd, d[j]*b[j]); if (s == (n - 1), return (1)); ); return (0); } \\ Michel Marcus, Aug 30 2013 CROSSREFS Cf. A005835, A000225, A005153, A103288. Sequence in context: A301587 A319796 A103288 * A092903 A005153 A174973 Adjacent sequences:  A125222 A125223 A125224 * A125226 A125227 A125228 KEYWORD nonn AUTHOR David Eppstein, Jan 13 2007 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 June 15 04:47 EDT 2021. Contains 345043 sequences. (Running on oeis4.)