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

%I A171487 #6 Aug 31 2013 02:31:46
%S A171487 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 A171487 2499,51,55,3135,57,1,63,4095,65,69,69,1,75,5775,77,81,81,85,7395,87,
%U A171487 91,8463,8835,95,99,99,1,105,105,1,111,111,115,13455,13923,14399,14883,15375
%N A171487 Product of odd prime anti-factors < n, with multiplicity.
%C A171487 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 A171487 In this sequence p < n, but p^k with k>=2 may be larger than n.
%C A171487 a(n) = 1 iff 2n-1 and 2n+1 are twin primes;
%C A171487 a(n) = 2n-1 iff 2n-1 is composite, 2n+1 is prime;
%C A171487 a(n) = 2n+1 iff 2n-1 is prime, 2n+1 is composite;
%C A171487 a(n) = (2n-1)(2n+1) iff 2n-1 and 2n+1 are both composite.
%H A171487 Daniel Forgues, <a href="/A171487/b171487.txt">Table of n, a(n) for n=1..49999</a>
%F A171487 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 A171487 GCD(a(n), a(n+1)) = {product of odd prime factors < 2n+1 of 2n+1, with multiplicity} (cf. A171435)
%e A171487 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 A171487 Cf. A171435, A130799, A066272.
%K A171487 nonn
%O A171487 1,4
%A A171487 _Daniel Forgues_, Dec 10 2009