A337112 Smallest term of A337081 that has exactly n prime factors, or 0 if no such term exists.

0, 4, 0, 90, 675, 1134, 6318, 4374, 32805, 255879, 1003833, 531441, 327544803, 20751953125, 225830078125, 91552734375, 1068115234375, 23651123046875, 316619873046875, 1697540283203125, 13256072998046875, 85353851318359375, 541210174560546875, 4518032073974609375, 58233737945556640625

Offset

1,2

Comments

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).

Links

Table of n, a(n) for n=1..25.

Crossrefs

Cf. A337113 (factors of terms).

Cf. A337037, A337080, A337081.

Cf. A056472 (all factorizations of n).

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).

Sequence in context: A358294 A298616 A366828 * A357560 A013037 A129814

Adjacent sequences: A337109 A337110 A337111 * A337113 A337114 A337115

Keyword

nonn

Author

Matej Veselovac, Aug 16 2020

Extensions

a(14) onward from David A. Corneth, Aug 26 2020

Status

approved