A353270 a(n) = gcd(n, A332449(n)), where A332449(n) = A005940(1+(3*A156552(n))).

1, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 13, 2, 3, 2, 17, 2, 19, 10, 3, 2, 23, 6, 5, 2, 3, 14, 29, 2, 31, 2, 3, 2, 5, 2, 37, 2, 3, 10, 41, 6, 43, 22, 3, 2, 47, 6, 7, 2, 3, 26, 53, 6, 5, 14, 3, 2, 59, 2, 61, 2, 21, 2, 5, 2, 67, 34, 3, 2, 71, 6, 73, 2, 3, 38, 7, 2, 79, 10, 3, 2, 83, 2, 5, 2, 3, 22, 89, 2, 7, 46, 3, 2, 5, 6

Offset: 1

Author

Antti Karttunen, Apr 09 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. A005940, A156552, A332449, A353271, A353272, A353274.

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)));
A353270(n) = gcd(n, A332449(n));

Formula

a(n) = gcd(n, A332449(n)) = gcd(n, A005940(1+(3*A156552(n)))).

a(n) = n / A353271(n) = A332449(n) / A353272(n).