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A171487 Product of odd prime anti-factors < 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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A166925 A178164 A216035 * A371996 A120704 A021506
KEYWORD
nonn
AUTHOR
Daniel Forgues, Dec 10 2009
STATUS
approved

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Last modified July 22 23:31 EDT 2024. Contains 374544 sequences. (Running on oeis4.)