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

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.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

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

Crossrefs

Positions of 1's in A325223.

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

Sequence in context: A128691 A359875 A028919 * A134620 A355791 A108315

Adjacent sequences: A325228 A325229 A325230 * A325232 A325233 A325234

Keyword

nonn

Author

Gus Wiseman, Apr 13 2019

Status

approved