A171435 Product of odd prime factors < n, with multiplicity.

1, 1, 1, 1, 1, 3, 1, 1, 9, 5, 1, 3, 1, 7, 15, 1, 1, 9, 1, 5, 21, 11, 1, 3, 25, 13, 27, 7, 1, 15, 1, 1, 33, 17, 35, 9, 1, 19, 39, 5, 1, 21, 1, 11, 45, 23, 1, 3, 49, 25, 51, 13, 1, 27, 55, 7, 57, 29, 1, 15, 1, 31, 63, 1, 65, 33, 1, 17, 69, 35, 1, 9, 1, 37, 75, 19, 77, 39, 1, 5, 81, 41, 1, 21, 85

Offset: 1

Author

Daniel Forgues, Dec 09 2009

Keywords

• nonn

Comments

In this sequence p < n, but p^k with k>=2 may be equal to n.

a(n) = 1 iff n = 2^k, k >= 0 or n is prime;

1 < a(n) < n iff n is even composite and not a power of 2;

a(n) = n iff n is nonprime (unit or composite) odd.

Links

• Daniel Forgues, Table of n, a(n) for n=1..100000

Crossrefs

Cf. A171487, A000265, A010051.

Programs

PARI

A171435(n) = if(isprime(n), 1, n>>valuation(n,2)); \\ Antti Karttunen, Mar 27 2022

Formula

If A010051(n) = 1 [when n is a prime], then a(n) = 1, otherwise a(n) = A000265(n). - Antti Karttunen, Mar 27 2022

Extensions

Edited by Daniel Forgues, Dec 10 2009