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

1,2

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).

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

Example

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.

Crossrefs

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

Sequence in context: A202400 A014793 A264305 * A206467 A264262 A232003

Adjacent sequences: A321334 A321335 A321336 * A321338 A321339 A321340

Keyword

nonn

Author

Charlie Neder, Nov 05 2018

Extensions

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

More terms from WG Zeist, Jan 09 2019

Status

approved