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a(n) is the least number with n factorizations into S-primes (numbers 4k+1 with no proper divisors > 1 of form 4m+1).
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%I #35 Jan 10 2019 22:35:54

%S 1,441,4389,39501,53361,92169,829521,1935549,302841,2725569,3041577,

%T 27374193,853577109,7682193981,3129357,6359661,19263321,234201429,

%U 230639102001,437200389130923862144165773,1341335457,12072019113,23318757,1201975929,28164213,253477917,4918230009,101711843982441

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

%C 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).

%H Charlie Neder, <a href="/A321337/b321337.txt">Table of n, a(n) for n = 1..277</a>

%H Charlie Neder, <a href="/A321337/a321337.txt">Table of n, a(n) for n = 1..600, missing 278 and 482</a>

%e 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.

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

%K nonn

%O 1,2

%A _Charlie Neder_, Nov 05 2018

%E a(13) corrected by _David A. Corneth_, Nov 10 2018

%E More terms from _WG Zeist_, Jan 09 2019