

A356064


Numbers with a prime index other than 1 that is not a primepower. Complement of A302492.


6



13, 26, 29, 37, 39, 43, 47, 52, 58, 61, 65, 71, 73, 74, 78, 79, 86, 87, 89, 91, 94, 101, 104, 107, 111, 113, 116, 117, 122, 129, 130, 137, 139, 141, 142, 143, 145, 146, 148, 149, 151, 156, 158, 163, 167, 169, 172, 173, 174, 178, 181, 182, 183, 185, 188, 193
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OFFSET

1,1


COMMENTS

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
These are numbers divisible by a prime number not of the form prime(q^k) where q is a prime number and k >= 1.


LINKS



EXAMPLE

The terms together with their prime indices begin:
13: {6}
26: {1,6}
29: {10}
37: {12}
39: {2,6}
43: {14}
47: {15}
52: {1,1,6}
58: {1,10}
61: {18}
65: {3,6}
71: {20}
73: {21}
74: {1,12}
78: {1,2,6}
79: {22}
86: {1,14}
87: {2,10}


MATHEMATICA

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], !And@@PrimePowerQ/@DeleteCases[primeMS[#], 1]&]


CROSSREFS

Heinz numbers of the partitions counted by A023893.
Allowing prime index 1 gives A356066.
A001222 counts primepower divisors.
A034699 gives the maximal primepower divisor.
A355742 chooses a primepower divisor of each prime index.
A355743 = numbers whose prime indices are primepowers, squarefree A356065.


KEYWORD

nonn


AUTHOR



STATUS

approved



