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

1,2

Comments

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

Links

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

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.

Example

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.

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A128039 A027428 A136850 * A280774 A083505 A099588

Adjacent sequences: A079245 A079246 A079247 * A079249 A079250 A079251

Keyword

nonn,easy

Author

Vladeta Jovovic, Feb 03 2003

Status

approved