A347120 Square root of the largest square dividing A005940(1+(3*A156552(n))): a(n) = A000188(A332449(n)).

1, 2, 3, 1, 5, 4, 7, 1, 1, 6, 11, 1, 13, 10, 9, 3, 17, 2, 19, 5, 15, 14, 23, 1, 1, 22, 1, 7, 29, 8, 31, 3, 21, 26, 25, 1, 37, 34, 33, 5, 41, 12, 43, 11, 1, 38, 47, 3, 1, 2, 39, 13, 53, 2, 35, 7, 51, 46, 59, 1, 61, 58, 7, 9, 55, 20, 67, 17, 57, 18, 71, 1, 73, 62, 3, 19, 49, 28, 79, 15, 5, 74, 83, 11, 65, 82, 69, 11, 89

Offset: 1

Author

Antti Karttunen, Aug 22 2021

Keywords

• nonn

Links

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

Crossrefs

Cf. A000188, A000196, A005940, A007913, A156552, A332449, A347119.

Programs

PARI

A000188(n) = core(n, 1)[2]; \\ This function from A000188
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)));
A347120(n) = A000188(A332449(n));

Formula

a(n) = A000188(A332449(n)).

a(n) = A000196(A332449(n)/A347119(n)).

a(p) = p for all primes p.