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A330949
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Odd nonprime numbers whose prime indices are not all prime numbers.
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5
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21, 35, 39, 49, 57, 63, 65, 69, 77, 87, 91, 95, 105, 111, 115, 117, 119, 129, 133, 141, 143, 145, 147, 159, 161, 169, 171, 175, 183, 185, 189, 195, 203, 207, 209, 213, 215, 217, 219, 221, 231, 235, 237, 245, 247, 253, 259, 261, 265, 267, 273, 285, 287, 291
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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.
Also MM-numbers of multiset partitions with at least two parts, not all of which are singletons (see example).
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LINKS
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EXAMPLE
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The sequence of terms together with their prime indices of prime indices begins:
21: {{1},{1,1}}
35: {{2},{1,1}}
39: {{1},{1,2}}
49: {{1,1},{1,1}}
57: {{1},{1,1,1}}
63: {{1},{1},{1,1}}
65: {{2},{1,2}}
69: {{1},{2,2}}
77: {{1,1},{3}}
87: {{1},{1,3}}
91: {{1,1},{1,2}}
95: {{2},{1,1,1}}
105: {{1},{2},{1,1}}
111: {{1},{1,1,2}}
115: {{2},{2,2}}
117: {{1},{1},{1,2}}
119: {{1,1},{4}}
129: {{1},{1,4}}
133: {{1,1},{1,1,1}}
141: {{1},{2,3}}
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MATHEMATICA
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Select[Range[1, 100, 2], !PrimeQ[#]&&!And@@PrimeQ/@PrimePi/@First/@If[#==1, {}, FactorInteger[#]]&]
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CROSSREFS
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Including even numbers gives A330948.
The number of prime prime indices is given by A257994.
The number of nonprime prime indices is given by A330944.
Primes of nonprime index are A007821.
Products of primes of prime index are A076610.
Products of primes of nonprime index are A320628.
The set S of numbers whose prime indices do not all belong to S is A324694.
Cf. A000040, A000720, A001222, A018252, A056239, A112798, A302242, A320629, A320633, A330943, A330947.
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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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