A353420 a(n) = A126760(A003961(n)).

1, 1, 2, 1, 3, 2, 4, 1, 9, 3, 5, 2, 6, 4, 12, 1, 7, 9, 8, 3, 19, 5, 10, 2, 17, 6, 42, 4, 11, 12, 13, 1, 22, 7, 26, 9, 14, 8, 29, 3, 15, 19, 16, 5, 59, 10, 18, 2, 41, 17, 32, 6, 20, 42, 31, 4, 39, 11, 21, 12, 23, 13, 92, 1, 40, 22, 24, 7, 49, 26, 25, 9, 27, 14, 82, 8, 48, 29, 28, 3, 209, 15, 30, 19, 45, 16, 52, 5, 33

Offset: 1

Author

Antti Karttunen, Apr 20 2022

Keywords

• nonn

Links

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

Crossrefs

Cf. A000265, A003602, A003961, A048673, A126760, A249735, A249745, A249746.

Cf. A353335 (Dirichlet inverse), A353336 (sum with it).

Programs

PARI

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A126760(n) = {n&&n\=3^valuation(n, 3)<A126760
A353420(n) = A126760(A003961(n));

Formula

a(n) = A126760(A003961(n)) = A249746(A003602(n)) = A126760(A249735(A003602(n))).

a(n) = A353336(4*n) = A353336(n) - A353335(n).

For all n >= 1, a(n) = a(2*n) = a(A000265(n)).

For all n >= 1, A249745(a(n)) = A003602(n).