A321337 a(n) is the least number with n factorizations into S-primes (numbers 4k+1 with no proper divisors > 1 of form 4m+1).

1, 441, 4389, 39501, 53361, 92169, 829521, 1935549, 302841, 2725569, 3041577, 27374193, 853577109, 7682193981, 3129357, 6359661, 19263321, 234201429, 230639102001, 437200389130923862144165773, 1341335457, 12072019113, 23318757, 1201975929, 28164213, 253477917, 4918230009, 101711843982441

Offset: 1

Author

Charlie Neder, Nov 05 2018

Keywords

• nonn

Comments

It suffices to check only numbers with all prime factors congruent to 3 mod 4 and continuous, nonincreasing prime exponents (i.e., members of the analog of A025487 with respect to primes congruent to 3 mod 4).

Examples

			a(4) = 39501 can be factored into S-primes (A057948) in 4 distinct ways: 9 * 21 * 209, 9 * 33 * 133, 9 * 57 * 77, or 21 * 33 * 57, and it is the smallest number with this property.
		

Links

• Charlie Neder, Table of n, a(n) for n = 1..277
• Charlie Neder, Table of n, a(n) for n = 1..600, missing 278 and 482

Crossrefs

Cf. A054520, A057948 (S-primes), A057949 (numbers with multiple factorizations into S-primes).

Extensions

a(13) corrected by David A. Corneth, Nov 10 2018

More terms from WG Zeist, Jan 09 2019