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Powers of superprimorials S(k)^m such that both k > 1 and m > 1, where S(n) = A006939(n).
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%I #5 Dec 30 2023 23:49:40

%S 144,1728,20736,129600,248832,2985984,35831808,46656000,429981696,

%T 5159780352,5715360000,16796160000,61917364224,743008370688,

%U 6046617600000,8916100448256,106993205379072,432081216000000,1283918464548864,2176782336000000,15407021574586368,30497732496000000

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

%C 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.

%H Michael De Vlieger, <a href="/A368508/b368508.txt">Table of n, a(n) for n = 1..1943</a>

%t 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]]

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

%K nonn,easy

%O 1,1

%A _Michael De Vlieger_, Dec 28 2023