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%I #7 Jul 29 2022 09:51:20
%S 13,26,29,37,39,43,47,52,58,61,65,71,73,74,78,79,86,87,89,91,94,101,
%T 104,107,111,113,116,117,122,129,130,137,139,141,142,143,145,146,148,
%U 149,151,156,158,163,167,169,172,173,174,178,181,182,183,185,188,193
%N Numbers with a prime index other than 1 that is not a prime-power. Complement of A302492.
%C 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.
%C These are numbers divisible by a prime number not of the form prime(q^k) where q is a prime number and k >= 1.
%e The terms together with their prime indices begin:
%e 13: {6}
%e 26: {1,6}
%e 29: {10}
%e 37: {12}
%e 39: {2,6}
%e 43: {14}
%e 47: {15}
%e 52: {1,1,6}
%e 58: {1,10}
%e 61: {18}
%e 65: {3,6}
%e 71: {20}
%e 73: {21}
%e 74: {1,12}
%e 78: {1,2,6}
%e 79: {22}
%e 86: {1,14}
%e 87: {2,10}
%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t Select[Range[100],!And@@PrimePowerQ/@DeleteCases[primeMS[#],1]&]
%Y Heinz numbers of the partitions counted by A023893.
%Y Allowing prime index 1 gives A356066.
%Y A000688 counts factorizations into prime-powers, strict A050361.
%Y A001222 counts prime-power divisors.
%Y A023894 counts partitions into prime-powers, strict A054685.
%Y A034699 gives the maximal prime-power divisor.
%Y A246655 lists the prime-powers (A000961 includes 1), towers A164336.
%Y A355742 chooses a prime-power divisor of each prime index.
%Y A355743 = numbers whose prime indices are prime-powers, squarefree A356065.
%Y Cf. A076610, A085970, A106244, A302492, A302493, A302601, A330946, A354911.
%K nonn
%O 1,1
%A _Gus Wiseman_, Jul 25 2022
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