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A304634
Numbers n with prime omicron 2, meaning A304465(n) = 2.
6
4, 6, 9, 10, 12, 14, 15, 18, 20, 21, 22, 24, 25, 26, 28, 33, 34, 35, 36, 38, 39, 40, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 65, 68, 69, 72, 74, 75, 76, 77, 80, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100, 104
OFFSET
1,1
COMMENTS
If n > 1 is not a prime number, we have A056239(n) >= Omega(n) >= omega(n) >= A071625(n) >= ... >= omicron(n) > 1 where Omega = A001222, omega = A001221, and omicron = A304465.
EXAMPLE
This is a list of normalized factorizations (see A112798) of selected entries:
4: {1,1}
6: {1,2}
12: {1,1,2}
24: {1,1,1,2}
36: {1,1,2,2}
48: {1,1,1,1,2}
60: {1,1,2,3}
72: {1,1,1,2,2}
96: {1,1,1,1,1,2}
120: {1,1,1,2,3}
144: {1,1,1,1,2,2}
180: {1,1,2,2,3}
192: {1,1,1,1,1,1,2}
216: {1,1,1,2,2,2}
240: {1,1,1,1,2,3}
288: {1,1,1,1,1,2,2}
384: {1,1,1,1,1,1,1,2}
420: {1,1,2,3,4}
432: {1,1,1,1,2,2,2}
480: {1,1,1,1,1,2,3}
576: {1,1,1,1,1,1,2,2}
768: {1,1,1,1,1,1,1,1,2}
840: {1,1,1,2,3,4}
864: {1,1,1,1,1,2,2,2}
960: {1,1,1,1,1,1,2,3}
MATHEMATICA
Join@@Position[Table[Switch[n, 1, 0, _?PrimeQ, 1, _, NestWhile[Sort[Length/@Split[#]]&, Sort[Last/@FactorInteger[n]], Length[#]>1&]//First], {n, 100}], 2]
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 15 2018
STATUS
approved