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A327908
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Nonprime squarefree numbers whose prime indices all have the same Omega (A001222) and the same sum of prime indices (A056239).
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6
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1, 667, 2021, 4331, 5767, 7081, 7663, 11021, 11639, 12091, 13837, 15049, 20413, 23213, 26123, 31553, 34933, 35657, 35723, 37909, 37979, 38021, 41449, 42919, 44197, 45113, 51019, 53531, 58339, 63407, 66013, 70531, 72929, 73373, 73903, 75763, 83411, 87361, 90581
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OFFSET
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1,2
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LINKS
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EXAMPLE
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The sequence of terms together with their prime indices begins:
1: {}
667: {9,10}
2021: {14,15}
4331: {18,20}
5767: {21,22}
7081: {21,25}
7663: {22,25}
11021: {27,28}
11639: {27,30}
12091: {28,30}
13837: {26,33}
15049: {26,35}
20413: {33,35}
23213: {34,39}
26123: {36,40}
31553: {34,49}
34933: {42,44}
35657: {42,45}
35723: {34,55}
37909: {39,49}
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MATHEMATICA
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primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[10000], !PrimeQ[#]&&SquareFreeQ[#]&&SameQ@@PrimeOmega/@primeMS[#]&&SameQ@@Total/@primeMS/@primeMS[#]&]
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CROSSREFS
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Equal sum of prime indices: A327901
Equal average of prime indices: A327902
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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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