A379833 - OEIS (original) (raw)

Multiplicative with a(p^e) = (p^2-1) * p^(4*e-2).

Dirichlet g.f.: zeta(s-4)/zeta(s-2).

In general, Dirichlet g.f. of J_k(n^m): zeta(s-m*k)/zeta(s-m*k+k), where J_k is the k-th Jordan totient function.

Sum_{i=1..n} a(i) ~ n^5 / (5*zeta(3)).

In general, Sum_{i=1..n} J_k(i^m) ~ n^(k*m+1) / ((k*m+1)*zeta(k+1)) for k,m >= 1.

Sum_{n>=1} 1/a(n) = (Pi^6/540) * Product_{p prime} (1 - 1/p^2 + 1/p^6) = 1.10666099915727116962...

In general, Sum_{n>=1} 1/J_k(n^m) = zeta(k) * zeta(k*m) * Product_{p prime} (1 - 1/p^k + 1/p^(k*m+k)), for k,m >= 2, and zeta(2) * zeta(m) * Product_{p prime} (1 - 1/p^2 + 1/p^(m+1) + 1/p^(m+2)) for k = 1 and m >= 2.

k*n^4 < a(n) < n^4 for n > 1, where k = 6/Pi^2 = 0.6079.... - Charles R Greathouse IV, Sep 29 2025