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A356064
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Numbers with a prime index other than 1 that is not a prime-power. Complement of A302492.
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6
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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
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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}
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MATHEMATICA
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primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], !And@@PrimePowerQ/@DeleteCases[primeMS[#], 1]&]
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CROSSREFS
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Heinz numbers of the partitions counted by A023893.
Allowing prime index 1 gives A356066.
A001222 counts prime-power divisors.
A034699 gives the maximal prime-power divisor.
A355742 chooses a prime-power divisor of each prime index.
A355743 = numbers whose prime indices are prime-powers, squarefree A356065.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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