A343826 Numbers which are the product of two S-primes (A057948) in exactly one way.

25, 45, 65, 81, 85, 105, 117, 145, 153, 165, 169, 185, 189, 205, 221, 245, 261, 265, 273, 285, 289, 297, 305, 333, 345, 357, 365, 369, 377, 385, 429, 445, 465, 477, 481, 485, 493, 505, 513, 533, 545, 549, 561, 565, 605, 609, 621, 629, 637, 645, 657, 665, 685

Offset: 1

Author

Zachary DeStefano, Apr 30 2021

Keywords

• nonn

Comments

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.

Examples

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

Links

• Zachary DeStefano, Table of n, a(n) for n = 1..3786

Crossrefs

Cf. A054520, A057948, A057949, A057950.

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

Programs

PARI

\\ uses is(n) from A057948
isok(n) = sumdiv(n, d, (d<=n/d) && is(d) && is(n/d)) == 1; \\ Michel Marcus, May 01 2021

Formula

a(n) == 1 (mod 4). - Hugo Pfoertner, May 01 2021