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 A360970 Multiplicative with a(p^e) = e^3, p prime and e > 0. 4
 1, 1, 1, 8, 1, 1, 1, 27, 8, 1, 1, 8, 1, 1, 1, 64, 1, 8, 1, 8, 1, 1, 1, 27, 8, 1, 27, 8, 1, 1, 1, 125, 1, 1, 1, 64, 1, 1, 1, 27, 1, 1, 1, 8, 8, 1, 1, 64, 8, 8, 1, 8, 1, 27, 1, 27, 1, 1, 1, 8, 1, 1, 8, 216, 1, 1, 1, 8, 1, 1, 1, 216, 1, 1, 8, 8, 1, 1, 1, 64, 64 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 Vaclav Kotesovec, Graph - the asymptotic ratio (10^9 terms) FORMULA Dirichlet g.f.: zeta(s) * Product_{primes p} (1 + (7*p^(2*s) - 2*p^s + 1) / (p^s*(p^s - 1)^3)). Sum_{k=1..n} a(k) ~ c * n, where c = Product_{primes p} (1 + (7*p^2 - 2*p + 1) / (p*(p-1)^3)) = 109.601930729008995813857898403091253809628920963774227252953... a(n) = A005361(n)^3. MAPLE f:= proc(n) local t; mul(t^3, t = ifactors(n)[2][.., 2]); end proc: map(f, [\$1..100]); # Robert Israel, Mar 29 2023 MATHEMATICA g[p_, e_] := e^3; a[1] = 1; a[n_] := Times @@ g @@@ FactorInteger[n]; Array[a, 100] PROG (PARI) for(n=1, 100, print1(direuler(p=2, n, (1 - 3*X + 10*X^2 - 3*X^3 + X^4)/(1-X)^4)[n], ", ")) CROSSREFS Cf. A005361, A226602, A360969, A361132. Sequence in context: A066341 A181064 A010153 * A363918 A133421 A128881 Adjacent sequences: A360967 A360968 A360969 * A360971 A360972 A360973 KEYWORD nonn,mult AUTHOR Vaclav Kotesovec, Feb 27 2023 STATUS approved

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Last modified April 19 06:44 EDT 2024. Contains 371782 sequences. (Running on oeis4.)