A343879
Number of pairs (d1, d2) of divisors of n such that d1
0, 0, 0, 1, 0, 2, 0, 3, 1, 2, 0, 7, 0, 2, 2, 6, 0, 7, 0, 7, 2, 2, 0, 15, 1, 2, 3, 7, 0, 12, 0, 10, 2, 2, 2, 19, 0, 2, 2, 15, 0, 12, 0, 7, 7, 2, 0, 26, 1, 7, 2, 7, 0, 15, 2, 15, 2, 2, 0, 31, 0, 2, 7, 15, 2, 12, 0, 7, 2, 12, 0, 37, 0, 2, 7, 7, 2, 12, 0, 26, 6, 2, 0, 31, 2, 2, 2, 15
Offset: 1
Keywords
Examples
a(12) = 7; The 7 pairs are (1,2), (1,3), (1,4), (1,6), (2,4), (2,6), (3,6).
Crossrefs
Cf. A343877.
Programs
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Mathematica
Table[Sum[Sum[(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, Floor[n/2]}], {n, 100}] -
PARI
a(n) = sumdiv(n, d1, sumdiv(n, d2, if ((d1 < d2) && (d1+d2 <= n) && !(d2 % d1), 1))); \\ Michel Marcus, May 02 2021
Formula
a(n) = Sum_{k=1..floor(n/2)} Sum_{i=1..k-1} c(k/i) * c(n/k) * c(n/i), where c(n) = 1 - ceiling(n) + floor(n).
Comments