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A343828 Numbers which are the product of two S-primes (A057948) in exactly three ways. 4
4389, 5313, 7161, 9177, 9933, 10857, 12369, 13629, 14421, 14973, 15477, 16401, 17157, 18249, 18753, 19173, 19437, 20769, 22701, 23529, 23541, 23793, 24717, 26733, 26961, 27993, 28329, 28497, 29337, 29469, 30261, 30597, 31521, 32109, 32361, 32637, 33117, 33649 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
There exist numbers which are the product of two S-primes in exactly 1, 2, and 3 ways.
An S-prime is either a prime of the form 4k+1 or a semiprime of the form (4k+3)*(4m+3). That means the maximum number of prime factors that a number factorizable into two S-primes can have is four (all 4k + 3), and those can be combined into S-primes in at most three distinct ways. - Gleb Ivanov, Dec 07 2021
LINKS
FORMULA
a(n) == 1 (mod 4). - Hugo Pfoertner, May 01 2021
EXAMPLE
9177 = 21*437 = 57*161 = 69*133 which are all S-primes (A057948), and admits no other S-Prime factorizations.
4389 = (3*7)*(11*19) = (3*11)*(7*19) = (3*19)*(7*11); 3,7,11,19 are the smallest primes of the form 4k + 3.
PROG
(PARI) \\ uses is(n) from A057948
isok(n) = sumdiv(n, d, (d<=n/d) && is(d) && is(n/d)) == 3; \\ Michel Marcus, May 01 2021
CROSSREFS
Exactly one way: A343826. Exactly two ways: A343827.
Sequence in context: A252645 A252858 A027506 * A345180 A345183 A345184
KEYWORD
nonn
AUTHOR
Zachary DeStefano, Apr 30 2021
STATUS
approved

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Last modified May 29 00:29 EDT 2024. Contains 372921 sequences. (Running on oeis4.)