A322901 Numbers whose prime indices are all powers of the same number.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 34, 36, 37, 38, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 52, 53, 54, 56, 57, 58, 59, 61, 62, 63, 64, 67, 68, 71, 72, 73, 74, 76, 79, 80, 81, 82, 83

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..67.

Example

The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k). The sequence of all integer partitions whose Heinz numbers belong to the sequence begins: (), (1), (2), (11), (3), (21), (4), (111), (22), (31), (5), (211), (6), (41), (1111), (7), (221), (8), (311), (42), (51), (9), (2111), (33), (61), (222), (411).

Mathematica

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
radbase[n_]:=n^(1/GCD@@FactorInteger[n][[All, 2]]);
Select[Range[100], SameQ@@radbase/@DeleteCases[primeMS[#], 1]&]

Crossrefs

Cf. A001597, A018819, A052409, A052410, A056239, A072720, A072721, A302242, A302593, A322900, A322902, A322903.

Sequence in context: A331995 A347457 A318991 * A322911 A023756 A080944

Adjacent sequences: A322898 A322899 A322900 * A322902 A322903 A322904

Keyword

nonn

Author

Gus Wiseman, Dec 30 2018

Status

approved