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

Author

Antti Karttunen, Nov 14 2017

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

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

Cf. A294900 (fixed points).

Programs

Mathematica

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

PARI

A294888(n) = sumdiv(n, d, (d
				

Formula

a(n) = Sum_{d|n, dA294935(d)*d.

a(n) + A294889(n) = A001065(n).