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A356064 Numbers with a prime index other than 1 that is not a prime-power. 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 (list; graph; refs; listen; history; text; internal format)
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.
A000688 counts factorizations into prime-powers, strict A050361.
A001222 counts prime-power divisors.
A023894 counts partitions into prime-powers, strict A054685.
A034699 gives the maximal prime-power divisor.
A246655 lists the prime-powers (A000961 includes 1), towers A164336.
A355742 chooses a prime-power divisor of each prime index.
A355743 = numbers whose prime indices are prime-powers, squarefree A356065.
Sequence in context: A095781 A037974 A318957 * A180055 A346003 A164007
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 25 2022
STATUS
approved

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Last modified October 2 20:27 EDT 2023. Contains 365840 sequences. (Running on oeis4.)