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

1,12

Comments

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

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences related to sums of divisors.

Formula

a(n) = Sum_{d|n, d<n} A294936(d)*d. - Typo in A-number corrected by Antti Karttunen, Apr 04 2022

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

Example

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.

Mathematica

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

Prog

(PARI) A294887(n) = sumdiv(n, d, (d<n)*(sigma(d)>=(2*d))*d);

Crossrefs

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

Sequence in context: A102638 A187794 A200214 * A331979 A005872 A035322

Adjacent sequences: A294884 A294885 A294886 * A294888 A294889 A294890

Keyword

nonn

Author

Antti Karttunen, Nov 14 2017

Status

approved