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A320325
Numbers whose product of prime indices is a perfect power.
24
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
OFFSET
1,1
COMMENTS
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.
EXAMPLE
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}}
MATHEMATICA
Select[Range[100], GCD@@FactorInteger[Times@@Cases[FactorInteger[#], {p_, k_}:>PrimePi[p]^k]][[All, 2]]>1&]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 10 2018
STATUS
approved