

A171487


Product of odd prime antifactors < n, with multiplicity.


2



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
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OFFSET

1,4


COMMENTS

Antifactor is here defined as almost synonym with antidivisor (except without the restriction of being less than n for antidivisor.) ODD p^k is antifactor (<n or >n) of n iff p^i, 1<=i<=k are antifactors of n (note that this only applies to ODD antifactors.)
In this sequence p < n, but p^k with k>=2 may be larger than n.
a(n) = 1 iff 2n1 and 2n+1 are twin primes;
a(n) = 2n1 iff 2n1 is composite, 2n+1 is prime;
a(n) = 2n+1 iff 2n1 is prime, 2n+1 is composite;
a(n) = (2n1)(2n+1) iff 2n1 and 2n+1 are both composite.


LINKS



FORMULA

a(n) = {product of odd prime factors < 2n1 of 2n1, 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 antifactor (and antidivisor) of 5, and 3^2=9 is also an antifactor (but not an antidivisor since > 5) of 5.


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



