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A304636
Numbers n with prime omicron 3, meaning A304465(n) = 3.
6
8, 27, 30, 42, 66, 70, 78, 102, 105, 110, 114, 125, 130, 138, 154, 165, 170, 174, 182, 186, 190, 195, 222, 230, 231, 238, 246, 255, 258, 266, 273, 282, 285, 286, 290, 310, 318, 322, 343, 345, 354, 357, 360, 366, 370, 374, 385, 399, 402, 406, 410, 418, 426
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:
8: {1,1,1}
30: {1,2,3}
360: {1,1,1,2,2,3}
720: {1,1,1,1,2,2,3}
900: {1,1,2,2,3,3}
1440: {1,1,1,1,1,2,2,3}
2160: {1,1,1,1,2,2,2,3}
2880: {1,1,1,1,1,1,2,2,3}
4320: {1,1,1,1,1,2,2,2,3}
5760: {1,1,1,1,1,1,1,2,2,3}
8640: {1,1,1,1,1,1,2,2,2,3}
Starting with A112798(1801800) and repeatedly taking the multiset of multiplicities we have {1,1,1,2,2,3,3,4,5,6} -> {1,1,1,2,2,3} -> {1,2,3} -> {1,1,1} -> {3}, so 1801800 belongs to the sequence.
MATHEMATICA
Join@@Position[Table[Switch[n, 1, 0, _?PrimeQ, 1, _, NestWhile[Sort[Length/@Split[#]]&, Sort[Last/@FactorInteger[n]], Length[#]>1&]//First], {n, 200}], 3]
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 15 2018
STATUS
approved