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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 27 12:49 EDT 2022. Contains 354097 sequences. (Running on oeis4.)