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A320325
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Numbers whose product of prime indices is a perfect power.
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24
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7, 9, 14, 18, 19, 21, 23, 25, 27, 28, 36, 38, 42, 46, 49, 50, 53, 54, 56, 57, 63, 72, 76, 81, 84, 92, 97, 98, 100, 103, 106, 108, 112, 114, 115, 121, 125, 126, 131, 133, 144, 147, 151, 152, 159, 161, 162, 168, 169, 171, 175, 183, 184, 185, 189, 194, 195, 196
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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.
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LINKS
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EXAMPLE
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The terms together with their corresponding multiset multisystems (A302242):
7: {{1,1}}
9: {{1},{1}}
14: {{},{1,1}}
18: {{},{1},{1}}
19: {{1,1,1}}
21: {{1},{1,1}}
23: {{2,2}}
25: {{2},{2}}
27: {{1},{1},{1}}
28: {{},{},{1,1}}
36: {{},{},{1},{1}}
38: {{},{1,1,1}}
42: {{},{1},{1,1}}
46: {{},{2,2}}
49: {{1,1},{1,1}}
50: {{},{2},{2}}
53: {{1,1,1,1}}
54: {{},{1},{1},{1}}
56: {{},{},{},{1,1}}
57: {{1},{1,1,1}}
63: {{1},{1},{1,1}}
72: {{},{},{},{1},{1}}
76: {{},{},{1,1,1}}
81: {{1},{1},{1},{1}}
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MATHEMATICA
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Select[Range[100], GCD@@FactorInteger[Times@@Cases[FactorInteger[#], {p_, k_}:>PrimePi[p]^k]][[All, 2]]>1&]
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CROSSREFS
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Cf. A000720, A001222, A001597, A003963, A056239, A064573, A112798, A302242, A305551, A306017, A319056, A319066, A320322, A320323, A320324.
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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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