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Product of odd prime anti-factors < n, with multiplicity.
2

%I #6 Aug 31 2013 02:31:46

%S 1,1,1,9,9,1,15,15,1,21,21,25,675,27,1,33,1155,35,39,39,1,45,45,49,

%T 2499,51,55,3135,57,1,63,4095,65,69,69,1,75,5775,77,81,81,85,7395,87,

%U 91,8463,8835,95,99,99,1,105,105,1,111,111,115,13455,13923,14399,14883,15375

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

%C 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.)

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

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

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

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

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

%H Daniel Forgues, <a href="/A171487/b171487.txt">Table of n, a(n) for n=1..49999</a>

%F 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}

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

%e 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.

%Y Cf. A171435, A130799, A066272.

%K nonn

%O 1,4

%A _Daniel Forgues_, Dec 10 2009