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Numbers of the form 2 * p or 3 * 2^k, p prime, k > 1.
4

%I #8 Apr 16 2019 17:31:21

%S 6,10,12,14,22,24,26,34,38,46,48,58,62,74,82,86,94,96,106,118,122,134,

%T 142,146,158,166,178,192,194,202,206,214,218,226,254,262,274,278,298,

%U 302,314,326,334,346,358,362,382,384,386,394,398,422,446,454,458,466

%N Numbers of the form 2 * p or 3 * 2^k, p prime, k > 1.

%C Also numbers n such that the sum of prime indices of n minus the greater of the number of prime factors of n counted with multiplicity and the largest prime index of n is 1. 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, and their sum is A056239.

%H Chai Wah Wu, <a href="/A325231/b325231.txt">Table of n, a(n) for n = 1..10000</a>

%e The sequence of terms together with their prime indices begins:

%e 6: {1,2}

%e 10: {1,3}

%e 12: {1,1,2}

%e 14: {1,4}

%e 22: {1,5}

%e 24: {1,1,1,2}

%e 26: {1,6}

%e 34: {1,7}

%e 38: {1,8}

%e 46: {1,9}

%e 48: {1,1,1,1,2}

%e 58: {1,10}

%e 62: {1,11}

%e 74: {1,12}

%e 82: {1,13}

%e 86: {1,14}

%e 94: {1,15}

%e 96: {1,1,1,1,1,2}

%e 106: {1,16}

%e 118: {1,17}

%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];

%t Select[Range[100],Total[primeMS[#]]-Max[Length[primeMS[#]],Max[primeMS[#]]]==1&]

%o (Python)

%o from sympy import isprime

%o A325231_list = [n for n in range(6,10**6) if ((not n % 2) and isprime(n//2)) or (bin(n)[2:4] == '11' and bin(n).count('1') == 2)] # _Chai Wah Wu_, Apr 16 2019

%Y Positions of 1's in A325223.

%Y Cf. A001222, A056239, A060687, A061395, A093641, A112798, A174090, A257541, A265283, A325224, A325225, A325227, A325232.

%K nonn

%O 1,1

%A _Gus Wiseman_, Apr 13 2019