A079248 Sum of q in all pairs (p,q), 0 <= p < q, p+q divides n.

1, 3, 6, 10, 13, 23, 23, 36, 41, 55, 52, 87, 71, 102, 110, 136, 118, 184, 146, 217, 204, 241, 211, 335, 260, 333, 328, 410, 331, 512, 377, 528, 482, 562, 512, 743, 533, 699, 666, 853, 652, 970, 716, 985, 927, 1018, 853, 1311, 948, 1252, 1124, 1367, 1081, 1578

Offset: 1

Author

Vladeta Jovovic, Feb 03 2003

Keywords

• nonn
• easy

Comments

Equals row sums of triangle A143444 (the inverse Mobius transform of a diagonalized matrix of A001318). - Gary W. Adamson, Aug 15 2008

Examples

			There are 7 pairs (p,q), 0 <= p < q, such that p+q divides 6: (0,1), (0,2), (0,3), (0,6), (1, 2), (1, 5), (2, 4); thus a(6) = 1+2+3+6+2+5+4 = 23.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harvey P. Dale)

Crossrefs

Cf. A143444. - Gary W. Adamson, Aug 15 2008

Programs

Mathematica

Table[Total[Select[Subsets[Range[0,n],{2}],Divisible[n,Total[#]]&][[All, 2]]],{n,60}] (* Harvey P. Dale, Oct 06 2019 *)

PARI

a(n) = {my(d = divisors(n)); 1 + sum(i = 2, #d, binomial(d[i] + 1, 2) - binomial(d[i]\2 + 1, 2))} \\ David A. Corneth, Oct 06 2019

Formula

Inverse Moebius transform of A001318.

G.f.: Sum_{n>1} x^n*(1+x^n+x^(2*n))/(1-x^n)/(1-x^(2*n))^2.