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A361204
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Positive integers k such that 2*omega(k) <= bigomega(k).
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6
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1, 4, 8, 9, 16, 24, 25, 27, 32, 36, 40, 48, 49, 54, 56, 64, 72, 80, 81, 88, 96, 100, 104, 108, 112, 121, 125, 128, 135, 136, 144, 152, 160, 162, 169, 176, 184, 189, 192, 196, 200, 208, 216, 224, 225, 232, 240, 243, 248, 250, 256, 272, 288, 289, 296, 297, 304
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OFFSET
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1,2
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LINKS
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FORMULA
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EXAMPLE
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The terms together with their prime indices begin:
1: {}
4: {1,1}
8: {1,1,1}
9: {2,2}
16: {1,1,1,1}
24: {1,1,1,2}
25: {3,3}
27: {2,2,2}
32: {1,1,1,1,1}
36: {1,1,2,2}
40: {1,1,1,3}
48: {1,1,1,1,2}
49: {4,4}
54: {1,2,2,2}
56: {1,1,1,4}
64: {1,1,1,1,1,1}
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MAPLE
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filter:= proc(n) local F, t;
F:= ifactors(n)[2];
add(t[2], t=F) >= 2*nops(F)
end proc:
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MATHEMATICA
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Select[Range[100], 2*PrimeNu[#]<=PrimeOmega[#]&]
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CROSSREFS
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These partitions are counted by A237363.
A001221 (omega) counts distinct prime factors.
A001222 (bigomega) counts prime factors.
Comparing twice the number of distinct parts to the number of parts:
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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