A368508 Powers of superprimorials S(k)^m such that both k > 1 and m > 1, where S(n) = A006939(n).

144, 1728, 20736, 129600, 248832, 2985984, 35831808, 46656000, 429981696, 5159780352, 5715360000, 16796160000, 61917364224, 743008370688, 6046617600000, 8916100448256, 106993205379072, 432081216000000, 1283918464548864, 2176782336000000, 15407021574586368, 30497732496000000

Offset: 1

Author

Michael De Vlieger, Dec 28 2023

Keywords

• nonn
• easy

Comments

Proper subset of A364930, which is the intersection of A286708 and A025487, and is in turn a proper subset of A364710. This is to say, a(n) is a product of primorials and is squareful and neither squarefree nor a prime power.

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..1943

Crossrefs

Cf. A002110 (squarefree kernels), A006939, A025487, A126706, A286708, A364930, A368507.

Programs

Mathematica

nn = 2^120; k = 2; P = 6; Q = 2 P; Union@ Reap[While[j = 2; While[Q^j < nn, Sow[Q^j]; j++]; j > 2, k++; P *= Prime[k]; Q *= P] ][[-1, 1]]