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

Author

Amiram Eldar, Aug 11 2023

Keywords

• nonn

Comments

First differs from A294888 at n = 48.

Links

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

Crossrefs

Cf. A001065, A118372, A181487, A294888.

Programs

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]

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<M. F. Hasler at A181487

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).