A319165 Perfect powers whose prime indices are not relatively prime.

9, 25, 27, 49, 81, 121, 125, 169, 243, 289, 343, 361, 441, 529, 625, 729, 841, 961, 1331, 1369, 1521, 1681, 1849, 2187, 2197, 2209, 2401, 2809, 3125, 3249, 3481, 3721, 3969, 4225, 4489, 4913, 5041, 5329, 6241, 6561, 6859, 6889, 7569, 7921, 8281, 9261, 9409

Offset: 1

Author

Gus Wiseman, Sep 12 2018

Keywords

• nonn

Comments

A prime index of n is a number m such that prime(m) divides n.

Examples

			The sequence of integer partitions whose Heinz numbers are in the sequence begins: (22), (33), (222), (44), (2222), (55), (333), (66), (22222), (77), (444), (88), (4422), (99), (3333), (222222).
		

Crossrefs

Cf. A001597, A056239, A072774, A181819, A289509, A296150, A298748, A319151, A319161, A319163, A319164.

Programs

Mathematica

Select[Range[10000],With[{t=Transpose[FactorInteger[#]]},And[GCD@@PrimePi/@t[[1]]>1,GCD@@t[[2]]>1]]&]