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A324929
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Numbers whose product of prime indices is even.
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18
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3, 6, 7, 9, 12, 13, 14, 15, 18, 19, 21, 24, 26, 27, 28, 29, 30, 33, 35, 36, 37, 38, 39, 42, 43, 45, 48, 49, 51, 52, 53, 54, 56, 57, 58, 60, 61, 63, 65, 66, 69, 70, 71, 72, 74, 75, 76, 77, 78, 79, 81, 84, 86, 87, 89, 90, 91, 93, 95, 96, 98, 99, 101, 102, 104
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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, with product A003963(n).
Also Heinz numbers of integer partitions whose product of parts is even (counted by A047967), where the Heinz number of an integer partition (y_1,...,y_k) is prime(y_1) * ... * prime(y_k).
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LINKS
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EXAMPLE
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The sequence of terms together with their prime indices begins:
3: {2}
6: {1,2}
7: {4}
9: {2,2}
12: {1,1,2}
13: {6}
14: {1,4}
15: {2,3}
18: {1,2,2}
19: {8}
21: {2,4}
24: {1,1,1,2}
26: {1,6}
27: {2,2,2}
28: {1,1,4}
29: {10}
30: {1,2,3}
33: {2,5}
35: {3,4}
36: {1,1,2,2}
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MATHEMATICA
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Select[Range[100], EvenQ[Times@@PrimePi/@If[#==1, {}, FactorInteger[#]][[All, 1]]]&]
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PROG
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(PARI) isok(n) = my(f=factor(n)[, 1]); !(prod(k=1, #f, primepi(f[k])) % 2); \\ Michel Marcus, Mar 22 2019
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CROSSREFS
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Cf. A000720, A001222, A003963, A005087, A033844, A047967, A066208, A112798, A257992, A318400, A324927.
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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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