A294888 Sum of nonabundant proper divisors of n.

0, 1, 1, 3, 1, 6, 1, 7, 4, 8, 1, 16, 1, 10, 9, 15, 1, 21, 1, 22, 11, 14, 1, 24, 6, 16, 13, 28, 1, 42, 1, 31, 15, 20, 13, 25, 1, 22, 17, 30, 1, 54, 1, 40, 33, 26, 1, 40, 8, 43, 21, 46, 1, 48, 17, 64, 23, 32, 1, 46, 1, 34, 41, 63, 19, 78, 1, 58, 27, 74, 1, 33, 1, 40, 49, 64, 19, 90, 1, 46, 40, 44, 1, 86, 23, 46, 33, 92, 1, 96, 21

Offset

1,4

Comments

Sum of divisors of n smaller than n that are nonabundant numbers (in A263837).

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} A294935(d)*d.

a(n) + A294889(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, 6, 9, 10, 15 and 45 are in A263837, thus a(90) = 1+2+3+5+6+9+10+15+45 = 96.

Mathematica

a[n_] := DivisorSum[n, Boole[# < n && DivisorSigma[1, #] <= 2#] * #&];
Array[a, 100] (* Jean-François Alcover, Nov 17 2017 *)

Prog

(PARI) A294888(n) = sumdiv(n, d, (d<n)*(sigma(d)<=(2*d))*d);

Crossrefs

Cf. A001065, A263837, A294928, A294935, A294886, A294887, A294889.

Cf. A294900 (fixed points).

Sequence in context: A294886 A357698 A069250 * A364858 A001065 A173455

Adjacent sequences: A294885 A294886 A294887 * A294889 A294890 A294891

Keyword

nonn

Author

Antti Karttunen, Nov 14 2017

Status

approved