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A372999
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a(n) = Sum_{k=1..n} tau( (n/gcd(k,n))^4 ).
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3
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1, 6, 11, 24, 21, 66, 31, 76, 65, 126, 51, 264, 61, 186, 231, 212, 81, 390, 91, 504, 341, 306, 111, 836, 201, 366, 299, 744, 141, 1386, 151, 548, 561, 486, 651, 1560, 181, 546, 671, 1596, 201, 2046, 211, 1224, 1365, 666, 231, 2332, 409, 1206, 891, 1464, 261, 1794
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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) = 5*p - 4.
a(n) = Sum_{d|n} phi(d) * tau(d^4).
Multiplicative with a(p^e) = (4 - (4*e+5)*p^e + (4*e+1)*p^(e+1))/(p-1). - Amiram Eldar, May 21 2024
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MATHEMATICA
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f[p_, e_] := (4 - (4*e+5)*p^e + (4*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^4));
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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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