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

Author

Antti Karttunen, Feb 21 2021

Keywords

• nonn

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)

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.

Programs

Mathematica

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

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)));

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.