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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 Table of n, a(n) for n=1..56. 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. Cf. A076610, A085970, A106244, A302492, A302493, A302601, A330946, A354911. Sequence in context: A095781 A037974 A318957 * A180055 A346003 A164007 Adjacent sequences: A356061 A356062 A356063 * A356065 A356066 A356067 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.)