A357050 Number of ways A005101(n)+1 can be written as sum of a subset of the proper divisors of A005101(n), the n-th abundant number.

2, 1, 1, 4, 4, 7, 2, 2, 10, 2, 2, 32, 2, 1, 26, 1, 6, 24, 1, 19, 20, 2, 1, 1, 20, 4, 1, 270, 11, 14, 1, 14, 116, 12, 9, 12, 3, 195, 1, 2, 719, 1, 42, 1, 8, 9, 8, 2, 148, 142, 6, 1, 8, 6, 6, 2154, 1, 534, 1, 6, 125, 108, 1, 6, 117, 1, 447, 4

Offset

1,1

Comments

Obviously, for non abundant numbers (including perfect numbers) N, there is no way to write N+1 as the sum of a subset of N's proper divisors. Therefore we consider only abundant N = A005101(n) here.

The first zero appears for the seventh weird and primitive weird number A006037(7) = A002975(7) = 9272 = A005101(2310) (which surprisingly is w = A100696(1), the first weird number such that the sum of its divisors less than its abundance A033880(w) is larger than that).

Links

Table of n, a(n) for n=1..68.

Prog

(PARI) {A357050(n)= sum(b=1, -1+2^#d=divisors(n)[^-1], vecsum(vecextract(d, b))==n+1)} \\ not very efficient, better use code as in is_A005835().

Crossrefs

Cf. A005101, A006037, A002975, A005835 (abundant, weird, primitive weird and pseudoperfect numbers).

Cf. A033880 (abundance), A100696.

Sequence in context: A336996 A222541 A177263 * A197380 A057785 A305882

Adjacent sequences: A357047 A357048 A357049 * A357051 A357052 A357053

Keyword

nonn

Author

M. F. Hasler, Dec 13 2022

Status

approved