A341619 Characteristic function of primitive nondeficient numbers (A006039): a(n) = 1 if proper multiples of n are all abundant, and proper divisors of n are all deficient, 0 otherwise.

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

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for characteristic functions

Index entries for sequences related to sigma(n)

Formula

a(n) = [A341620(n) == 1], where [ ] is the Iverson bracket.

a(n) = 1 iff A341620(n) = 1.

Mathematica

a[n_] := Boole[DivisorSum[n, 1 &, DivisorSigma[1, #] >= 2*# &] == 1]; Array[a, 100] (* Amiram Eldar, Feb 22 2021 *)

Prog

(PARI) A341619(n) = if(sigma(n)<(2*n), 0, fordiv(n, d, if((d<n)&&(sigma(d) >= 2*d), return(0))); (1)); \\ After code in A071395

Crossrefs

Cf. A006039, A071395, A337690 (inverse Möbius transform), A341620.

Cf. also A341609.

Sequence in context: A177063 A378529 A378448 * A378537 A379475 A302049

Adjacent sequences: A341616 A341617 A341618 * A341620 A341621 A341622

Keyword

nonn

Author

Antti Karttunen, Feb 21 2021

Status

approved