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A360911
Multiplicative with a(p^e) = 3*e - 2.
6
1, 1, 1, 4, 1, 1, 1, 7, 4, 1, 1, 4, 1, 1, 1, 10, 1, 4, 1, 4, 1, 1, 1, 7, 4, 1, 7, 4, 1, 1, 1, 13, 1, 1, 1, 16, 1, 1, 1, 7, 1, 1, 1, 4, 4, 1, 1, 10, 4, 4, 1, 4, 1, 7, 1, 7, 1, 1, 1, 4, 1, 1, 4, 16, 1, 1, 1, 4, 1, 1, 1, 28, 1, 1, 4, 4, 1, 1, 1, 10, 10, 1, 1, 4
OFFSET
1,4
LINKS
FORMULA
Dirichlet g.f.: zeta(s)^2 * Product_{primes p} (1 - 1/p^s + 3/p^(2*s)).
Dirichlet g.f.: zeta(s) * Product_{primes p} (1 + 3/(p^s*(p^s-1))).
Sum_{k=1..n} a(k) ~ c*n, where c = Product_{primes p} (1 + 3/(p*(p-1))) = 5.092999766083306437144607885642959667401184716827970969797879646796872425...
MATHEMATICA
a[n_] := Times @@ ((3*Last[#] - 2) & /@ FactorInteger[n]); a[1] = 1; Array[a, 100] (* Amiram Eldar, Feb 25 2023 *)
PROG
(PARI) for(n=1, 100, print1(direuler(p=2, n, (1-X+3*X^2)/(1-X)^2)[n], ", "))
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Vaclav Kotesovec, Feb 25 2023
STATUS
approved