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A359905
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Numbers whose prime indices and prime signature both have integer mean.
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12
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2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 16, 17, 19, 21, 22, 23, 25, 27, 29, 30, 31, 32, 34, 37, 39, 41, 43, 46, 47, 49, 53, 55, 57, 59, 61, 62, 64, 67, 71, 73, 78, 79, 81, 82, 83, 85, 87, 88, 89, 91, 94, 97, 100, 101, 103, 105, 107, 109, 110, 111, 113, 115, 118, 121
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OFFSET
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1,1
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COMMENTS
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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.
A number's prime signature (row n of A124010) is the sequence of positive exponents in its prime factorization.
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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:
2: {1} 19: {8} 39: {2,6}
3: {2} 21: {2,4} 41: {13}
4: {1,1} 22: {1,5} 43: {14}
5: {3} 23: {9} 46: {1,9}
7: {4} 25: {3,3} 47: {15}
8: {1,1,1} 27: {2,2,2} 49: {4,4}
9: {2,2} 29: {10} 53: {16}
10: {1,3} 30: {1,2,3} 55: {3,5}
11: {5} 31: {11} 57: {2,8}
13: {6} 32: {1,1,1,1,1} 59: {17}
16: {1,1,1,1} 34: {1,7} 61: {18}
17: {7} 37: {12} 62: {1,11}
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MATHEMATICA
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prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
prisig[n_]:=If[n==1, {}, Last/@FactorInteger[n]];
Select[Range[100], IntegerQ[Mean[prix[#]]]&&IntegerQ[Mean[prisig[#]]]&]
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CROSSREFS
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A067340 lists numbers whose prime signature has integer mean.
A316413 lists numbers whose prime indices have integer mean.
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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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