A318471 -id:A318471 - cp's OEIS frontend

A318472 Multiplicative with a(p^e) = 2^A000045(e).

1, 2, 2, 2, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 4, 8, 2, 4, 2, 4, 4, 4, 2, 8, 2, 4, 4, 4, 2, 8, 2, 32, 4, 4, 4, 4, 2, 4, 4, 8, 2, 8, 2, 4, 4, 4, 2, 16, 2, 4, 4, 4, 2, 8, 4, 8, 4, 4, 2, 8, 2, 4, 4, 256, 4, 8, 2, 4, 4, 8, 2, 8, 2, 4, 4, 4, 4, 8, 2, 16, 8, 4, 2, 8, 4, 4, 4, 8, 2, 8, 4, 4, 4, 4, 4, 64, 2, 4, 4, 4, 2, 8, 2, 8, 8

Offset: 1

Antti Karttunen, Aug 29 2018

Antti Karttunen, Table of n, a(n) for n = 1..16384
Index entries for sequences computed from exponents in factorization of n

Cf. A000045, A318471, A318474.

A318472(n) = factorback(apply(e -> 2^fibonacci(e),factor(n)[,2]));

a(n) = 2^A318471(n).

A318473 Additive with a(p^e) = A000045(e+1).

Original entry on oeis.org

0, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 3, 1, 2, 2, 5, 1, 3, 1, 3, 2, 2, 1, 4, 2, 2, 3, 3, 1, 3, 1, 8, 2, 2, 2, 4, 1, 2, 2, 4, 1, 3, 1, 3, 3, 2, 1, 6, 2, 3, 2, 3, 1, 4, 2, 4, 2, 2, 1, 4, 1, 2, 3, 13, 2, 3, 1, 3, 2, 3, 1, 5, 1, 2, 3, 3, 2, 3, 1, 6, 5, 2, 1, 4, 2, 2, 2, 4, 1, 4, 2, 3, 2, 2, 2, 9, 1, 3, 3, 4, 1, 3, 1, 4, 3

Offset: 1

Antti Karttunen, Aug 29 2018

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for sequences computed from exponents in factorization of n.

Cf. A000045, A077761, A318471, A318474.

Differs from A008481 for the first time at n=32, where a(32)=8, while A008481(32)=7.

a[n_] := Total@ Fibonacci[FactorInteger[n][[;; , 2]] + 1]; a[1] = 0; Array[a, 100] (* Amiram Eldar, May 15 2023 *)

A318473(n) = vecsum(apply(e -> fibonacci(1+e),factor(n)[,2]));

a(n) = A007814(A318474(n)).

Sum_{k=1..n} a(k) ~ n * (log(log(n)) + B + C), where B is Mertens's constant (A077761) and C = Sum_{k>=2} Fibonacci(k-1) * P(k) = 1.30985781707683753402..., where P(s) is the prime zeta function. - Amiram Eldar, Oct 09 2023

cp's OEIS Frontend

A318472 Multiplicative with a(p^e) = 2^A000045(e).

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