A171487 Product of odd prime anti-factors < n, with multiplicity.

1, 1, 1, 9, 9, 1, 15, 15, 1, 21, 21, 25, 675, 27, 1, 33, 1155, 35, 39, 39, 1, 45, 45, 49, 2499, 51, 55, 3135, 57, 1, 63, 4095, 65, 69, 69, 1, 75, 5775, 77, 81, 81, 85, 7395, 87, 91, 8463, 8835, 95, 99, 99, 1, 105, 105, 1, 111, 111, 115, 13455, 13923, 14399, 14883, 15375

Offset: 1

Author

Daniel Forgues, Dec 10 2009

Keywords

• nonn

Comments

Anti-factor is here defined as almost synonym with anti-divisor (except without the restriction of being less than n for anti-divisor.) ODD p^k is anti-factor (n) of n iff p^i, 1<=i<=k are anti-factors of n (note that this only applies to ODD anti-factors.)

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

a(n) = 1 iff 2n-1 and 2n+1 are twin primes;

a(n) = 2n-1 iff 2n-1 is composite, 2n+1 is prime;

a(n) = 2n+1 iff 2n-1 is prime, 2n+1 is composite;

a(n) = (2n-1)(2n+1) iff 2n-1 and 2n+1 are both composite.

Examples

			3 is an anti-factor (and anti-divisor) of 5, and 3^2=9 is also an anti-factor (but not an anti-divisor since > 5) of 5.
		

Links

• Daniel Forgues, Table of n, a(n) for n=1..49999

Crossrefs

Cf. A171435, A130799, A066272.

Formula

a(n) = {product of odd prime factors < 2n-1 of 2n-1, with multiplicity} * {product of odd prime factors < 2n+1 of 2n+1, with multiplicity}

GCD(a(n), a(n+1)) = {product of odd prime factors < 2n+1 of 2n+1, with multiplicity} (cf. A171435)