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A340933
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Numbers whose least prime index is even. Heinz numbers of integer partitions whose last part is even.
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9
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3, 7, 9, 13, 15, 19, 21, 27, 29, 33, 37, 39, 43, 45, 49, 51, 53, 57, 61, 63, 69, 71, 75, 77, 79, 81, 87, 89, 91, 93, 99, 101, 105, 107, 111, 113, 117, 119, 123, 129, 131, 133, 135, 139, 141, 147, 151, 153, 159, 161, 163, 165, 169, 171, 173, 177, 181, 183
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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. 1 has no prime indices so is not counted.
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LINKS
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FORMULA
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Closed under multiplication.
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EXAMPLE
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The sequence of terms together with their prime indices begins:
3: {2} 51: {2,7} 99: {2,2,5}
7: {4} 53: {16} 101: {26}
9: {2,2} 57: {2,8} 105: {2,3,4}
13: {6} 61: {18} 107: {28}
15: {2,3} 63: {2,2,4} 111: {2,12}
19: {8} 69: {2,9} 113: {30}
21: {2,4} 71: {20} 117: {2,2,6}
27: {2,2,2} 75: {2,3,3} 119: {4,7}
29: {10} 77: {4,5} 123: {2,13}
33: {2,5} 79: {22} 129: {2,14}
37: {12} 81: {2,2,2,2} 131: {32}
39: {2,6} 87: {2,10} 133: {4,8}
43: {14} 89: {24} 135: {2,2,2,3}
45: {2,2,3} 91: {4,6} 139: {34}
49: {4,4} 93: {2,11} 141: {2,15}
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MATHEMATICA
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Select[Range[2, 100], EvenQ[PrimePi[FactorInteger[#][[1, 1]]]]&]
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CROSSREFS
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These partitions are counted by A026805.
A061395 selects greatest prime index.
A112798 lists the prime indices of each positive integer.
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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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