A294886 Sum of deficient proper divisors of n.

0, 1, 1, 3, 1, 6, 1, 7, 4, 8, 1, 10, 1, 10, 9, 15, 1, 15, 1, 22, 11, 14, 1, 18, 6, 16, 13, 28, 1, 36, 1, 31, 15, 20, 13, 19, 1, 22, 17, 30, 1, 48, 1, 40, 33, 26, 1, 34, 8, 43, 21, 46, 1, 42, 17, 36, 23, 32, 1, 40, 1, 34, 41, 63, 19, 72, 1, 58, 27, 74, 1, 27, 1, 40, 49, 64, 19, 84, 1, 46, 40, 44, 1, 52, 23, 46, 33, 92, 1, 90, 21

Offset

1,4

Comments

Sum of divisors of n smaller than n that are deficient numbers (in A005100).

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} A294934(d)*d.

a(n) = A187793(n) - (A294934(n)*n).

a(n) + A294887(n) = A001065(n).

Example

Proper divisors of 90 are: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45. Of these 1, 2, 3, 5, 9, 10, 15 and 45 are in A005100, thus a(90) = 1+2+3+5+9+10+15+45 = 90.

Mathematica

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

Prog

(PARI) A294886(n) = sumdiv(n, d, (d<n)*(sigma(d)<(2*d))*d);

Crossrefs

Cf. A001065, A005100, A001065, A187793, A294926, A294934, A294887, A294888, A294889.

Cf. A125310 (fixed points).

Sequence in context: A134689 A248029 A117552 * A357698 A069250 A294888

Adjacent sequences: A294883 A294884 A294885 * A294887 A294888 A294889

Keyword

nonn

Author

Antti Karttunen, Nov 14 2017

Status

approved