A253275 a(n) = Sum_{i=1..floor(n/2)} d( i*(n-i) ), where d(n) = the number of divisors of n.

0, 1, 2, 5, 7, 9, 14, 17, 20, 23, 32, 31, 43, 41, 45, 53, 67, 57, 80, 71, 80, 87, 108, 91, 116, 113, 122, 121, 155, 121, 172, 153, 164, 171, 183, 165, 225, 203, 211, 201, 261, 205, 280, 241, 245, 271, 318, 253, 324, 287, 317, 309, 379, 305, 363, 335, 374

Offset

1,3

Comments

For each partition of n into 2 parts, multiply the parts together and find the number of divisors of each product formed. Then add the results to get a(n).

Links

Muniru A Asiru, Table of n, a(n) for n = 1..5000

Index entries for sequences related to partitions

Formula

a(n) = Sum_{i=1..A004526(n)} A000005( i*(n-i) ).

Maple

with(numtheory): A253275:=n->add(tau(i*(n-i)), i=1..floor(n/2)): seq(A253275(n), n=1..100);

Mathematica

Table[Sum[DivisorSigma[0, i (n - i)], {i, 1, Floor[n/2]}], {n, 100}]

Prog

(PARI) a(n) = sum(i=1, n\2, numdiv(i*(n-i))); \\ Michel Marcus, Mar 18 2016
(GAP) List([1..10^4], n->Sum([1..Int(n/2)], i->Tau(i*(n-i)))); # Muniru A Asiru, Feb 04 2018

Crossrefs

Cf. A000005.

Sequence in context: A333178 A169867 A287363 * A093417 A286162 A286164

Adjacent sequences: A253272 A253273 A253274 * A253276 A253277 A253278

Keyword

nonn,easy

Author

Wesley Ivan Hurt, May 01 2015

Status

approved