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 A333976 Number of pairs of divisors of n, (d1,d2), such that d1 <= d2 and gcd(d1,d2) > 1. 1

%I

%S 0,1,1,3,1,5,1,6,3,5,1,13,1,5,5,10,1,13,1,13,5,5,1,25,3,5,6,13,1,22,1,

%T 15,5,5,5,32,1,5,5,25,1,22,1,13,13,5,1,41,3,13,5,13,1,25,5,25,5,5,1,

%U 55,1,5,13,21,5,22,1,13,5,22,1,60,1,5,13,13,5,22,1,41,10

%N Number of pairs of divisors of n, (d1,d2), such that d1 <= d2 and gcd(d1,d2) > 1.

%F a(n) = Sum_{d1|n, d2|n, d1<=d2} (1-[gcd(d1,d2) = 1]), where [ ] is the Iverson bracket.

%e a(7) = 1; (7,7)

%e a(8) = 6; (2,2), (2,4), (2,8), (4,4), (4,8), (8,8)

%e a(9) = 3; (3,3), (3,9), (9,9)

%e a(10) = 5; (2,2), (2,10), (5,5), (5,10), (10,10)

%t Table[Sum[Sum[(1 - KroneckerDelta[GCD[i, k], 1]) (1 - Ceiling[n/k] + Floor[n/k]) (1 - Ceiling[n/i] + Floor[n/i]), {i, k}], {k, n}], {n, 100}]

%Y Cf. A275387 (same with d1<d2), A337298.

%K nonn

%O 1,4

%A _Wesley Ivan Hurt_, Jan 01 2021

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Last modified May 27 16:48 EDT 2022. Contains 354110 sequences. (Running on oeis4.)