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A302496
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Products of distinct primes of prime-power index.
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3
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1, 2, 3, 5, 6, 7, 10, 11, 14, 15, 17, 19, 21, 22, 23, 30, 31, 33, 34, 35, 38, 41, 42, 46, 51, 53, 55, 57, 59, 62, 66, 67, 69, 70, 77, 82, 83, 85, 93, 95, 97, 102, 103, 105, 106, 109, 110, 114, 115, 118, 119, 123, 127, 131, 133, 134, 138, 154, 155, 157, 159
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OFFSET
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1,2
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COMMENTS
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A prime index of n is a number m such that prime(m) divides n.
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LINKS
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EXAMPLE
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Entry A302242 describes a correspondence between positive integers and multiset multisystems. In this case it gives the following sequence of constant-multiset systems.
01: {}
02: {{}}
03: {{1}}
05: {{2}}
06: {{},{1}}
07: {{1,1}}
10: {{},{2}}
11: {{3}}
14: {{},{1,1}}
15: {{1},{2}}
17: {{4}}
19: {{1,1,1}}
21: {{1},{1,1}}
22: {{},{3}}
23: {{2,2}}
30: {{},{1},{2}}
31: {{5}}
33: {{1},{3}}
34: {{},{4}}
35: {{2},{1,1}}
38: {{},{1,1,1}}
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MATHEMATICA
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Select[Range[nn], Or[#===1, SquareFreeQ[#]&&And@@PrimePowerQ/@PrimePi/@DeleteCases[FactorInteger[#][[All, 1]], 2]]&]
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PROG
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(PARI) is(n) = if(bigomega(n)!=omega(n), return(0), my(f=factor(n)[, 1]~); for(k=1, #f, if(!isprimepower(primepi(f[k])) && primepi(f[k])!=1, return(0)))); 1 \\ Felix Fröhlich, Apr 10 2018
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CROSSREFS
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Cf. A000961, A001222, A003963, A005117, A007716, A056239, A275024, A279786, A281113, A296131, A301767, A302242, A302243, A302493, A302494.
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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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