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A319180
Perfect powers whose prime indices are relatively prime.
1
4, 8, 16, 32, 36, 64, 100, 128, 144, 196, 216, 225, 256, 324, 400, 484, 512, 576, 676, 784, 900, 1000, 1024, 1089, 1156, 1225, 1296, 1444, 1600, 1728, 1764, 1936, 2025, 2048, 2116, 2304, 2500, 2601, 2704, 2744, 2916, 3025, 3136, 3364, 3375, 3600, 3844, 4096
OFFSET
1,1
COMMENTS
A prime index of n is a number m such that prime(m) divides n.
EXAMPLE
The sequence of integer partitions whose Heinz numbers are in the sequence begins: (11), (111), (1111), (11111), (2211), (111111), (3311), (1111111), (221111), (4411), (222111), (3322), (11111111), (222211), (331111), (5511), (111111111), (22111111), (6611), (441111), (332211), (333111).
MATHEMATICA
Select[Range[1000], And[GCD@@PrimePi/@FactorInteger[#][[All, 1]]==1, GCD@@FactorInteger[#][[All, 2]]>1]&]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 12 2018
STATUS
approved