A347119 Squarefree part of A005940(1+(3*A156552(n))): a(n) = A007913(A332449(n)).

1, 1, 1, 10, 1, 1, 1, 30, 21, 1, 1, 22, 1, 1, 1, 10, 1, 10, 1, 10, 1, 1, 1, 66, 55, 1, 105, 10, 1, 1, 1, 30, 1, 1, 1, 154, 1, 1, 1, 30, 1, 1, 1, 10, 39, 1, 1, 22, 91, 21, 1, 10, 1, 30, 1, 30, 1, 1, 1, 34, 1, 1, 21, 10, 1, 1, 1, 10, 1, 1, 1, 462, 1, 1, 21, 10, 1, 1, 1, 10, 21, 1, 1, 22, 1, 1, 1, 30, 1, 22, 1, 10

Offset: 1

Author

Antti Karttunen, Aug 22 2021

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..12000
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A000290, A005117 (positions of 1's), A005940, A007913, A156552, A332449, A347120.

Programs

PARI

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
A156552(n) = { my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };
A332449(n) = A005940(1+(3*A156552(n)));
A347119(n) = core(A332449(n));

Formula

a(n) = A007913(A332449(n)).

a(n) = A332449(n) / A000290(A347120(n)).