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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.
6
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
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
KEYWORD
nonn,changed
AUTHOR
Jaroslav Krizek, Nov 09 2013
EXTENSIONS
Name edited and data section extended to a(105) by Antti Karttunen, Jan 19 2025
STATUS
approved