A353272 a(n) = A332449(n) / gcd(n, A332449(n)), where A332449(n) = A005940(1+(3*A156552(n))).

1, 2, 3, 5, 5, 8, 7, 15, 7, 18, 11, 11, 13, 50, 27, 45, 17, 20, 19, 25, 75, 98, 23, 11, 11, 242, 35, 35, 29, 32, 31, 135, 147, 338, 125, 77, 37, 578, 363, 75, 41, 24, 43, 55, 13, 722, 47, 33, 13, 42, 507, 65, 53, 20, 245, 105, 867, 1058, 59, 17, 61, 1682, 49, 405, 605, 200, 67, 85, 1083, 162, 71, 77, 73, 1922, 63

Offset: 1

Author

Antti Karttunen, Apr 09 2022

Keywords

• nonn
• look

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, A353271, A353273, A353274 [= gcd(n, a(n))].

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)));
A353272(n) = { my(u=A332449(n)); (u / gcd(n, u)); };

Formula

a(n) = A332449(n) / A353270(n) = A332449(n) / gcd(n, A332449(n)).

a(p) = p for all primes p.