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

1,3

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Index entries for sequences computed from indices in prime factorization

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).

Prog

(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)<<valuation(n, 2); n%3+n\6*2}; \\ From A126760
A353420(n) = A126760(A003961(n));

Crossrefs

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

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

Sequence in context: A261401 A373938 A217669 * A123021 A317056 A346699

Adjacent sequences: A353417 A353418 A353419 * A353421 A353422 A353423

Keyword

nonn

Author

Antti Karttunen, Apr 20 2022

Status

approved