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

1,4

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 or >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.

Links

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

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)

Example

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.

Crossrefs

Cf. A171435, A130799, A066272.

Sequence in context: A166925 A178164 A216035 * A371996 A120704 A021506

Adjacent sequences: A171484 A171485 A171486 * A171488 A171489 A171490

Keyword

nonn

Author

Daniel Forgues, Dec 10 2009

Status

approved