A368682 Products of primorials that are perfect powers but not prime powers.

36, 144, 216, 576, 900, 1296, 1728, 2304, 3600, 5184, 7776, 9216, 13824, 14400, 20736, 27000, 32400, 36864, 44100, 46656, 57600, 82944, 110592, 129600, 147456, 176400, 186624, 216000, 230400, 248832, 279936, 331776, 373248, 518400, 589824, 705600, 746496, 810000

Offset

1,1

Comments

Intersection of A025487 and A131605.

Proper subset of A286708.

Contains A365308 (perfect powers of composite primorials) and A368508 (perfect powers of composite superprimorials).

These numbers are perfect powers of some smaller product of primorials.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Formula

This sequence is { A368681 \ A000079 }.

Example

b(n) = A025487(n).
a(1) = b(11) = 36 = 6^2 = b(4)^2,
a(2) = b(19) = 144 = 12^2 = b(6)^2,
a(3) = b(23) = 216 = 6^3 = b(4)^3,
a(4) = b(33) = 576 = 24^2 = b(8)^2,
a(5) = b(38) = 900 = 30^2 = b(9)^2, etc.

Mathematica

Select[Range[36, 2^18, 2], And[Union@ Differences@ PrimePi@ #1 == {1}, AllTrue[Union@ Differences@ #2, # <= 0 &], GCD @@ #2 > 1] & @@ Transpose@ FactorInteger[#] &]

Crossrefs

Cf. A000079, A000961, A001597, A002110, A025487, A131605, A286708, A365308, A368508, A368681.

Sequence in context: A138202 A204106 A049227 * A016910 A005017 A288488

Adjacent sequences: A368679 A368680 A368681 * A368683 A368684 A368685

Keyword

nonn

Author

Michael De Vlieger, Jan 02 2024

Status

approved