A353271 a(n) = n / gcd(n, A332449(n)), where A332449(n) = A005940(1+(3*A156552(n))).

1, 1, 1, 2, 1, 3, 1, 4, 3, 5, 1, 6, 1, 7, 5, 8, 1, 9, 1, 2, 7, 11, 1, 4, 5, 13, 9, 2, 1, 15, 1, 16, 11, 17, 7, 18, 1, 19, 13, 4, 1, 7, 1, 2, 15, 23, 1, 8, 7, 25, 17, 2, 1, 9, 11, 4, 19, 29, 1, 30, 1, 31, 3, 32, 13, 33, 1, 2, 23, 35, 1, 12, 1, 37, 25, 2, 11, 39, 1, 8, 27, 41, 1, 42, 17, 43, 29, 4, 1, 45, 13, 2, 31

Offset: 1

Author

Antti Karttunen, Apr 09 2022

Keywords

• nonn
• less

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, A353270.

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)));
A353271(n) = (n / gcd(n, A332449(n)));

Formula

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