A337112 - OEIS

%I #24 May 08 2021 02:25:47

%S 0,4,0,90,675,1134,6318,4374,32805,255879,1003833,531441,327544803,

%T 20751953125,225830078125,91552734375,1068115234375,23651123046875,

%U 316619873046875,1697540283203125,13256072998046875,85353851318359375,541210174560546875,4518032073974609375,58233737945556640625

%N Smallest term of A337081 that has exactly n prime factors, or 0 if no such term exists.

%C a(n) is the smallest product of n primes that has unordered factorizations whose sums of factors are the same (is a term of A337080) and all of whose proper divisors have the complementary property: that every unordered factorization has a distinct sum of factors (i.e., all proper divisors are terms of A337037).

%Y Cf. A337113 (factors of terms).

%Y Cf. A337037, A337080, A337081.

%Y Cf. A056472 (all factorizations of n).

%Y Cf. r-almost primes: A000040 (r = 1), A001358 (r = 2), A014612 (r = 3), A014613 (r = 4), A014614 (r = 5), A046306 (r = 6), A046308 (r = 7), A046310 (r = 8), A046312 (r = 9), A046314 (r = 10), A069272 (r = 11), A069273 (r = 12), A069274 (r = 13), A069275 (r = 14), A069276 (r = 15), A069277 (r = 16), A069278 (r = 17), A069279 (r = 18), A069280 (r = 19), A069281 (r = 20).

%K nonn

%O 1,2

%A _Matej Veselovac_, Aug 16 2020

%E a(14) onward from _David A. Corneth_, Aug 26 2020