cp's OEIS Frontend

A325231 Numbers of the form 2 * p or 3 * 2^k, p prime, k > 1.

%I A325231 #8 Apr 16 2019 17:31:21
%S A325231 6,10,12,14,22,24,26,34,38,46,48,58,62,74,82,86,94,96,106,118,122,134,
%T A325231 142,146,158,166,178,192,194,202,206,214,218,226,254,262,274,278,298,
%U A325231 302,314,326,334,346,358,362,382,384,386,394,398,422,446,454,458,466
%N A325231 Numbers of the form 2 * p or 3 * 2^k, p prime, k > 1.
%C A325231 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 A325231 Chai Wah Wu, <a href="/A325231/b325231.txt">Table of n, a(n) for n = 1..10000</a>
%e A325231 The sequence of terms together with their prime indices begins:
%e A325231     6: {1,2}
%e A325231    10: {1,3}
%e A325231    12: {1,1,2}
%e A325231    14: {1,4}
%e A325231    22: {1,5}
%e A325231    24: {1,1,1,2}
%e A325231    26: {1,6}
%e A325231    34: {1,7}
%e A325231    38: {1,8}
%e A325231    46: {1,9}
%e A325231    48: {1,1,1,1,2}
%e A325231    58: {1,10}
%e A325231    62: {1,11}
%e A325231    74: {1,12}
%e A325231    82: {1,13}
%e A325231    86: {1,14}
%e A325231    94: {1,15}
%e A325231    96: {1,1,1,1,1,2}
%e A325231   106: {1,16}
%e A325231   118: {1,17}
%t A325231 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A325231 Select[Range[100],Total[primeMS[#]]-Max[Length[primeMS[#]],Max[primeMS[#]]]==1&]
%o A325231 (Python)
%o A325231 from sympy import isprime
%o A325231 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 A325231 Positions of 1's in A325223.
%Y A325231 Cf. A001222, A056239, A060687, A061395, A093641, A112798, A174090, A257541, A265283, A325224, A325225, A325227, A325232.
%K A325231 nonn
%O A325231 1,1
%A A325231 _Gus Wiseman_, Apr 13 2019