A343827 Numbers which are the product of two S-primes (A057948) in exactly two ways.

441, 693, 1089, 1197, 1449, 1617, 1881, 1953, 2277, 2541, 2709, 2793, 2961, 3069, 3249, 3381, 3717, 3933, 4221, 4257, 4473, 4557, 4653, 4761, 4977, 5229, 5301, 5841, 5929, 6321, 6417, 6489, 6633, 6741, 6897, 6909, 7029, 7353, 7581, 7821, 8001, 8037, 8217, 8253

Offset: 1

Author

Zachary DeStefano, Apr 30 2021

Keywords

• nonn

Comments

First differs from A057950 at a(21)=4473, whereas A057950(21)=4389, which can be represented as the product of two S-primes in exactly 3 ways.

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

			1449=9*161=21*69 which are all S-primes (A057948), and admits no other S-prime factorizations.
		

Links

• Zachary DeStefano, Table of n, a(n) for n = 1..2484

Crossrefs

Cf. A054520, A057948, A057949, A057950.

Exactly one way: A343826. Exactly three ways: A343828.

Programs

PARI

\\ uses is(n) from A057948
isok(n) = sumdiv(n, d, (d<=n/d) && is(d) && is(n/d)) == 2; \\ Michel Marcus, May 01 2021

Formula

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