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
Zachary DeStefano, Table of n, a(n) for n = 1..1014
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
KEYWORD
nonn
AUTHOR
Zachary DeStefano, Apr 30 2021
STATUS
approved