login
Numbers which are the product of two S-primes (A057948) in exactly one way.
4

%I #24 May 26 2021 02:53:15

%S 25,45,65,81,85,105,117,145,153,165,169,185,189,205,221,245,261,265,

%T 273,285,289,297,305,333,345,357,365,369,377,385,429,445,465,477,481,

%U 485,493,505,513,533,545,549,561,565,605,609,621,629,637,645,657,665,685

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

%C There exist numbers which are the product of two S-primes in exactly 1, 2, and 3 ways; however, it is unknown if any numbers exist which are the product of two S-primes in exactly 4 ways.

%H Zachary DeStefano, <a href="/A343826/b343826.txt">Table of n, a(n) for n = 1..3786</a>

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

%e 153 = 9*17 which are both S-primes, and admits no other S-prime factorizations.

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

%o isok(n) = sumdiv(n, d, (d<=n/d) && is(d) && is(n/d)) == 1; \\ _Michel Marcus_, May 01 2021

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

%Y Exactly two ways: A343827. Exactly three ways: A343828.

%K nonn

%O 1,1

%A _Zachary DeStefano_, Apr 30 2021