A337329 Sum of the products of all pairs of divisors of n, (d1,d2), such that d1|n, d2|n, d1|d2 and d1<d2.

0, 2, 3, 14, 5, 41, 7, 70, 39, 87, 11, 245, 13, 149, 143, 310, 17, 455, 19, 539, 241, 321, 23, 1165, 155, 431, 390, 945, 29, 1521, 31, 1302, 509, 699, 467, 2639, 37, 857, 679, 2595, 41, 2687, 43, 2093, 1664, 1221, 47, 5053, 399, 2387, 1091, 2835, 53, 4370, 951, 4585, 1333, 1887, 59

Offset

1,2

Comments

Total area of all distinct nonsquare rectangles that can be made whose side lengths are divisors of n and whose length is an integer multiple of its width.

Links

Table of n, a(n) for n=1..59.

Formula

a(n) = Sum_{d1|n, d2|n, d1|d2, d1<d2} d1*d2.

a(n) = n if and only if n is prime. - Bernard Schott, Aug 24 2020

Mathematica

Table[Sum[Sum[(i*k) (1 - Ceiling[k/i] + Floor[k/i])*(1 - Ceiling[n/k] + Floor[n/k]) (1 - Ceiling[n/i] + Floor[n/i]), {i, k - 1}], {k, n}], {n, 80}]

Crossrefs

Cf. A001001, A119616.

Sequence in context: A352407 A364037 A321226 * A329365 A119616 A286968

Adjacent sequences: A337326 A337327 A337328 * A337330 A337331 A337332

Keyword

nonn

Author

Wesley Ivan Hurt, Aug 23 2020

Status

approved