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A325231
Numbers of the form 2 * p or 3 * 2^k, p prime, k > 1.
4
6, 10, 12, 14, 22, 24, 26, 34, 38, 46, 48, 58, 62, 74, 82, 86, 94, 96, 106, 118, 122, 134, 142, 146, 158, 166, 178, 192, 194, 202, 206, 214, 218, 226, 254, 262, 274, 278, 298, 302, 314, 326, 334, 346, 358, 362, 382, 384, 386, 394, 398, 422, 446, 454, 458, 466
OFFSET
1,1
COMMENTS
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.
EXAMPLE
The sequence of terms together with their prime indices begins:
6: {1,2}
10: {1,3}
12: {1,1,2}
14: {1,4}
22: {1,5}
24: {1,1,1,2}
26: {1,6}
34: {1,7}
38: {1,8}
46: {1,9}
48: {1,1,1,1,2}
58: {1,10}
62: {1,11}
74: {1,12}
82: {1,13}
86: {1,14}
94: {1,15}
96: {1,1,1,1,1,2}
106: {1,16}
118: {1,17}
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], Total[primeMS[#]]-Max[Length[primeMS[#]], Max[primeMS[#]]]==1&]
PROG
(Python)
from sympy import isprime
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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 13 2019
STATUS
approved