A357050 - OEIS

%I #4 Dec 15 2022 13:52:57

%S 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,

%T 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,

%U 2154,1,534,1,6,125,108,1,6,117,1,447,4

%N 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.

%C 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.

%C 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).

%o (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().

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

%Y Cf. A033880 (abundance), A100696.

%K nonn

%O 1,1

%A _M. F. Hasler_, Dec 13 2022