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A327902
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Nonprime squarefree numbers whose prime indices all have the same average of prime indices (A326567/A326568).
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3
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1, 21, 57, 115, 133, 145, 159, 371, 393, 399, 515, 535, 565, 667, 803, 869, 917, 933, 1007, 1067, 1113, 1963, 2021, 2095, 2157, 2165, 2177, 2249, 2285, 2315, 2363, 2369, 2461, 2489, 2599, 2705, 2751, 2839, 2987, 3021, 3103, 3277, 3335, 3707, 3859, 4331, 4367
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OFFSET
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1,2
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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.
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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: {}
21: {2,4}
57: {2,8}
115: {3,9}
133: {4,8}
145: {3,10}
159: {2,16}
371: {4,16}
393: {2,32}
399: {2,4,8}
515: {3,27}
535: {3,28}
565: {3,30}
667: {9,10}
803: {5,21}
869: {5,22}
917: {4,32}
933: {2,64}
1007: {8,16}
1067: {5,25}
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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[1000], !PrimeQ[#]&&SquareFreeQ[#]&&SameQ@@Mean/@primeMS/@primeMS[#]&];
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CROSSREFS
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The version including primes and nonsquarefree numbers is A326536.
The version for number of prime indices is A327900.
The version for sum of prime indices is A327901.
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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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