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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
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).
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
KEYWORD
nonn
AUTHOR
M. F. Hasler, Dec 13 2022
STATUS
approved