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

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

Author

Wesley Ivan Hurt, Aug 23 2020

Keywords

• nonn

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.

Crossrefs

Cf. A001001, A119616.

Programs

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}]

Formula

a(n) = Sum_{d1|n, d2|n, d1|d2, d1

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

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