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A253275
a(n) = Sum_{i=1..floor(n/2)} d( i*(n-i) ), where d(n) = the number of divisors of n.
2
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).
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
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, May 01 2015
STATUS
approved