cp's OEIS Frontend

A365308 Powers of primorials P(k)^m, k > 1, m > 1, where P(k) = A002110(k).

%I A365308 #57 Mar 10 2024 04:19:48
%S A365308 36,216,900,1296,7776,27000,44100,46656,279936,810000,1679616,5336100,
%T A365308 9261000,10077696,24300000,60466176,362797056,729000000,901800900,
%U A365308 1944810000,2176782336,12326391000,13060694016,21870000000,78364164096,260620460100,408410100000,470184984576
%N A365308 Powers of primorials P(k)^m, k > 1, m > 1, where P(k) = A002110(k).
%C A365308 Proper subset of A303606, in turn a proper subset of A286708, in turn a proper subset of A126706.
%C A365308 Numbers in A322793 that are not powers of 2.
%H A365308 Michael De Vlieger, <a href="/A365308/b365308.txt">Table of n, a(n) for n = 1..4935</a>
%H A365308 Michael De Vlieger, <a href="/A365308/a365308.png">1024 X 1024 Bitmap</a> showing A322793(n) in black if a power of 2 (i.e., in A000079) else white if in this sequence, n = 1..2^20, arranged from left to right in rows, then from top to bottom.
%F A365308 Intersection of A100778 and A303606.
%F A365308 This sequence is {A325374 \ {A002110 \ {1,2}}} = {A322793 \ {A000079 \ {1,2}}}.
%F A365308 Sum_{n>=1} 1/a(n) = Sum_{k>=2} 1/(P(k)*(P(k)-1)) = 0.03450573145072369022... . - _Amiram Eldar_, Mar 10 2024
%e A365308 Terms less than 10^4 include P(2)^2 = 36, P(2)^3 = 216, P(2)^4 = 1296, P(2)^5 = 7776, and P(3)^2 = 900.
%t A365308 nn = 2^39; k = 2; P = 6; Union@ Reap[While[j = 2; While[P^j < nn, Sow[P^j]; j++]; j > 2, k++; P *= Prime[k]] ][[-1, 1]]
%Y A365308 Cf. A000079, A002110, A100778, A126706, A286708, A303606, A322793, A325374.
%K A365308 nonn,easy
%O A365308 1,1
%A A365308 _Michael De Vlieger_, Oct 02 2023