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A062368
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Multiplicative with a(p^e) = (e+1)*(e+2)*(4*e+3)/6.
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4
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1, 7, 7, 22, 7, 49, 7, 50, 22, 49, 7, 154, 7, 49, 49, 95, 7, 154, 7, 154, 49, 49, 7, 350, 22, 49, 50, 154, 7, 343, 7, 161, 49, 49, 49, 484, 7, 49, 49, 350, 7, 343, 7, 154, 154, 49, 7, 665, 22, 154, 49, 154, 7, 350, 49, 350, 49, 49, 7, 1078, 7, 49, 154, 252, 49, 343, 7, 154
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OFFSET
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1,2
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COMMENTS
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Conjecture: this is the third inverse Mobius transform of the sequence 4^A001221(n). - R. J. Mathar, Aug 09 2012
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LINKS
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FORMULA
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a(n) = Sum_{i|n, j|n} tau(i)*tau(j)/tau(gcd(i, j)), where tau(n) = number of divisors of n, cf. A000005.
Also a(n) = Sum_{i|n, j|n} tau(lcm(i, j)).
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MATHEMATICA
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f[p_, e_] := (e+1)*(e+2)*(4*e+3)/6; a[n_] := Times @@ f @@@ FactorInteger[n]; a[1] = 1; Array[a, 100] (* Amiram Eldar, Sep 05 2023 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy,mult
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AUTHOR
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STATUS
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approved
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