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A372997
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a(n) = Sum_{k=1..n} tau( (n/gcd(k,n))^3 ).
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3
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1, 5, 9, 19, 17, 45, 25, 59, 51, 85, 41, 171, 49, 125, 153, 163, 65, 255, 73, 323, 225, 205, 89, 531, 157, 245, 231, 475, 113, 765, 121, 419, 369, 325, 425, 969, 145, 365, 441, 1003, 161, 1125, 169, 779, 867, 445, 185, 1467, 319, 785, 585, 931, 209, 1155, 697, 1475
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OFFSET
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1,2
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LINKS
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FORMULA
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If p is prime, a(p) = 4*p - 3.
a(n) = Sum_{d|n} phi(d) * tau(d^3).
Multiplicative with a(p^e) = (3 - (3*e+4)*p^e + (3*e+1)*p^(e+1))/(p-1). - Amiram Eldar, May 21 2024
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MATHEMATICA
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f[p_, e_] := (3 - (3*e+4)*p^e + (3*e+1)*p^(e+1))/(p-1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, May 21 2024 *)
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PROG
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(PARI) a(n) = sumdiv(n, d, eulerphi(d)*numdiv(d^3));
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CROSSREFS
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KEYWORD
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nonn,mult
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AUTHOR
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STATUS
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approved
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