A231367 a(n) = 1 if A024816(m) = n has a solution for some m, where A024816(m) = sums of non-divisors of m = antisigma(m), otherwise 0.

1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1

Offset

0

Links

Antti Karttunen, Table of n, a(n) for n = 0..20197

Index entries for characteristic functions.

Formula

a(A231368(n)) = 1, a(A231369(n)) = 0.

a(n) = 1 if A024816(m) = n for any m, else 0.

a(n) = 1 for such n that A231366(n) >= 1, a(n) = 0 for such n that A231366(n) = 0.

Example

a(2) = 1 because there is number m with antisigma(m) = 2; m = 3.

Prog

(PARI)
up_to = 105;
A024816(n) = (n*(n+1)/2-sigma(n));
A231367list(up_to) = { my(v=vector(1+up_to), u); for(n=1, 2+up_to, if((u = A024816(n))<=up_to, v[1+u] = 1)); (v); };
v231367 = A231367list(up_to);
A231367(n) = v231367[1+n]; \\ Antti Karttunen, Jan 19 2025

Crossrefs

Characteristic function of A231368.

Cf. A175192 (characteristic function of numbers k such that sigma(m) = k has solution), A231365, A231366, A231369.

Sequence in context: A152065 A267870 A267878 * A113428 A133101 A258769

Adjacent sequences: A231364 A231365 A231366 * A231368 A231369 A231370

Keyword

nonn

Author

Jaroslav Krizek, Nov 09 2013

Extensions

Name edited and data section extended to a(105) by Antti Karttunen, Jan 19 2025

Status

approved