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

36, 216, 900, 1296, 7776, 27000, 44100, 46656, 279936, 810000, 1679616, 5336100, 9261000, 10077696, 24300000, 60466176, 362797056, 729000000, 901800900, 1944810000, 2176782336, 12326391000, 13060694016, 21870000000, 78364164096, 260620460100, 408410100000, 470184984576

Offset: 1

Author

Michael De Vlieger, Oct 02 2023

Keywords

• nonn
• easy

Comments

Proper subset of A303606, in turn a proper subset of A286708, in turn a proper subset of A126706.

Numbers in A322793 that are not powers of 2.

Examples

			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.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..4935
• Michael De Vlieger, 1024 X 1024 Bitmap 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.

Crossrefs

Cf. A000079, A002110, A100778, A126706, A286708, A303606, A322793, A325374.

Programs

Mathematica

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]]

Formula

Intersection of A100778 and A303606.

This sequence is {A325374 \ {A002110 \ {1,2}}} = {A322793 \ {A000079 \ {1,2}}}.

Sum_{n>=1} 1/a(n) = Sum_{k>=2} 1/(P(k)*(P(k)-1)) = 0.03450573145072369022... . - Amiram Eldar, Mar 10 2024