A294887 Sum of nondeficient proper divisors of n.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 36, 0, 0, 0, 20, 0, 6, 0, 0, 0, 0, 0, 42, 0, 0, 0, 0, 0, 24, 0, 28, 0, 0, 0, 68, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 6, 0, 60, 0, 0, 0, 88, 0, 0, 0, 0, 0, 54, 0, 0, 0, 0, 0, 90, 0, 0, 0, 20, 0, 6, 0, 0, 0

Offset: 1

Author

Antti Karttunen, Nov 14 2017

Keywords

• nonn

Comments

Sum of divisors n smaller than n that are nondeficient numbers (in A023196).

Examples

			Proper divisors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, and 45. Of these 6, 18 and 30 are in A023196, thus a(90) = 6+18+30 = 54.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences related to sums of divisors.

Crossrefs

Cf. A001065, A023196, A294927, A294936, A294886, A294888, A294889.

Programs

Mathematica

a[n_] := DivisorSum[n, # &, # < n && DivisorSigma[1, #] >= 2*# &]; Array[a, 100] (* Amiram Eldar, Mar 14 2024 *)

PARI

A294887(n) = sumdiv(n, d, (d=(2*d))*d);

Formula

a(n) = Sum_{d|n, dA294936(d)*d. - Typo in A-number corrected by Antti Karttunen, Apr 04 2022

a(n) + A294886(n) = A001065(n).