A294930 Characteristic function for A091191, primitive abundant numbers: abundant numbers (A005101) having no abundant proper divisor.

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

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..67004

Index entries for characteristic functions.

Formula

a(n) = A294937(n) * [0==A294929(n)].

a(n) = 1 iff A080224(n) = 1.

Mathematica

a[n_] := Boole[Count[Divisors[n], _?(DivisorSigma[1, #] > 2*# &)] == 1]; Array[a, 100] (* Amiram Eldar, Mar 18 2024 *)

Prog

(PARI) A294930(n) = if(sigma(n)<=2*n, 0, fordiv(n, d, if(d<n && sigma(d)>2*d, return(0))); (1)); \\ edited by Antti Karttunen, Sep 07 2025

Crossrefs

Cf. A005101, A080224, A091191, A187795, A294890, A294929, A294937, A341619.

Sequence in context: A065202 A374100 A323547 * A353472 A359475 A396865

Adjacent sequences: A294927 A294928 A294929 * A294931 A294932 A294933

Keyword

nonn

Author

Antti Karttunen, Nov 14 2017

Status

approved