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Numbers which are the product of two S-primes (A057948) in exactly three ways.
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%I #35 Dec 30 2021 14:36:58

%S 4389,5313,7161,9177,9933,10857,12369,13629,14421,14973,15477,16401,

%T 17157,18249,18753,19173,19437,20769,22701,23529,23541,23793,24717,

%U 26733,26961,27993,28329,28497,29337,29469,30261,30597,31521,32109,32361,32637,33117,33649

%N Numbers which are the product of two S-primes (A057948) in exactly three ways.

%C There exist numbers which are the product of two S-primes in exactly 1, 2, and 3 ways.

%C 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

%H Zachary DeStefano, <a href="/A343828/b343828.txt">Table of n, a(n) for n = 1..1014</a>

%F a(n) == 1 (mod 4). - _Hugo Pfoertner_, May 01 2021

%e 9177 = 21*437 = 57*161 = 69*133 which are all S-primes (A057948), and admits no other S-Prime factorizations.

%e 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.

%o (PARI) \\ uses is(n) from A057948

%o isok(n) = sumdiv(n, d, (d<=n/d) && is(d) && is(n/d)) == 3; \\ _Michel Marcus_, May 01 2021

%Y Cf. A054520, A057948, A057949, A057950.

%Y Exactly one way: A343826. Exactly two ways: A343827.

%K nonn

%O 1,1

%A _Zachary DeStefano_, Apr 30 2021