A343877
Number of pairs (d1, d2) of divisors of n such that d1
0, 0, 0, 1, 0, 3, 0, 3, 1, 3, 0, 10, 0, 3, 3, 6, 0, 10, 0, 10, 3, 3, 0, 21, 1, 3, 3, 10, 0, 21, 0, 10, 3, 3, 3, 28, 0, 3, 3, 21, 0, 21, 0, 10, 10, 3, 0, 36, 1, 10, 3, 10, 0, 21, 3, 21, 3, 3, 0, 55, 0, 3, 10, 15, 3, 21, 0, 10, 3, 21, 0, 55, 0, 3, 10, 10, 3, 21, 0, 36, 6, 3, 0, 55
Offset: 1
Keywords
Examples
a(12) = 10; The 10 pairs are (1,2), (1,3), (1,4), (1,6), (2,3), (2,4), (2,6), (3,4), (3,6), (4,6).
Programs
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Mathematica
Table[Sum[Sum[(1 - Ceiling[n/k] + Floor[n/k]) (1 - Ceiling[n/i] + Floor[n/i]), {i, k - 1}], {k, Floor[n/2]}], {n, 100}] -
PARI
a(n) = sumdiv(n, d1, sumdiv(n, d2, if ((d1 < d2) && (d1+d2 <= n), 1))); \\ Michel Marcus, May 02 2021
Formula
a(n) = Sum_{k=1..floor(n/2)} Sum_{i=1..k-1} c(n/k) * c(n/i), where c(n) = 1 - ceiling(n) + floor(n).
a(n) = (1/2)*tau(n)^2 - (3/2)*tau(n) + 1. - Ridouane Oudra, May 29 2025
Comments