A364858 a(n) = Sum_{d|n, d < n, d in S} d, where S is the set defined in A118372.

0, 1, 1, 3, 1, 6, 1, 7, 4, 8, 1, 16, 1, 10, 9, 15, 1, 21, 1, 22, 11, 14, 1, 24, 6, 16, 13, 28, 1, 42, 1, 31, 15, 20, 13, 25, 1, 22, 17, 30, 1, 54, 1, 40, 33, 26, 1, 64, 8, 43, 21, 46, 1, 48, 17, 64, 23, 32, 1, 46, 1, 34, 41, 63, 19, 78, 1, 58, 27, 74, 1, 93, 1

Offset

1,4

Comments

First differs from A294888 at n = 48.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) <= A001065(n).

a(n) <= n if and only if n is in the set S.

a(n) = n if and only if n is S-perfect (A118372).

a(n) > n if and only if n is S-abundant (A181487).

Mathematica

seq[nmax_] := Module[{s = {1}, a = {0}, sum}, Do[sum = Total[Select[Divisors[n], MemberQ[s, #] &]]; If[sum <= n, AppendTo[s, n]]; AppendTo[a, sum], {n, 2, nmax}]; a]; seq[100]

Prog

(PARI) lista(nmax) = {my(c = 0, s); print1(0, ", "); for(n=2, nmax, s = sumdiv(n, d, !bittest(c, d)*d) - n; if(s > n, c+=1<<n); print1(s, ", ")); } \\ after M. F. Hasler at A181487

Crossrefs

Cf. A001065, A118372, A181487, A294888.

Sequence in context: A357698 A069250 A294888 * A001065 A173455 A324535

Adjacent sequences: A364855 A364856 A364857 * A364859 A364860 A364861

Keyword

nonn

Author

Amiram Eldar, Aug 11 2023

Status

approved