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

1,1

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.

Links

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

Formula

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

Example

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

Prog

(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

Crossrefs

Cf. A054520, A057948, A057949, A057950.

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

Sequence in context: A252194 A057949 A057950 * A250808 A202400 A014793

Adjacent sequences: A343824 A343825 A343826 * A343828 A343829 A343830

Keyword

nonn

Author

Zachary DeStefano, Apr 30 2021

Status

approved