A341620 Number of nondeficient divisors of n.

0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 3, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 3, 0, 2, 0, 0, 0, 5, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 6, 0, 0, 0, 0, 0, 2, 0, 3, 0, 0, 0, 5, 0, 0, 0, 1, 0, 4, 0, 0, 0, 0, 0, 5, 0, 0, 0, 2, 0, 2, 0, 1, 0, 0, 0, 6, 0, 0, 0, 3, 0, 2, 0, 0, 0, 0, 0, 8

Offset

1,12

Comments

Number of nondeficient numbers (A023196) dividing n.

Links

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

Index entries for sequences related to sigma(n)

Formula

a(n) = Sum_{d|n} A294936(d).

a(n) = A294927(n) + A294936(n).

a(n) = A080224(n) + A080225(n) = A000005(n) - A080226(n).

a(n) >= A337690(n) for all n.

a(n) = 1 iff A341619(n) = 1.

Mathematica

a[n_] := DivisorSum[n, 1 &, DivisorSigma[1, #] >= 2*# &]; Array[a, 120] (* Amiram Eldar, Feb 22 2021 *)

Prog

(PARI)
A294936(n) = (sigma(n, -1)>=2); \\ From A294936.
A341620(n) = sumdiv(n, d, A294936(d));
(PARI) A341620(n) = sumdiv(n, d, (sigma(d)>=(2*d)));

Crossrefs

Cf. A000005, A006039 (positions of ones), A023196, A080224, A080225, A080226, A294927, A294936, A337690, A341619.

Differs from a derived sequence A341624 for the first time at n=120, where a(120)=8, while A341624(120)=1.

Sequence in context: A028649 A305558 A341624 * A097798 A065205 A036272

Adjacent sequences: A341617 A341618 A341619 * A341621 A341622 A341623

Keyword

nonn

Author

Antti Karttunen, Feb 21 2021

Status

approved