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A302496 Products of distinct primes of prime-power index. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A prime index of n is a number m such that prime(m) divides n.

LINKS

Table of n, a(n) for n=1..61.

EXAMPLE

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}}

MATHEMATICA

Select[Range[nn], Or[#===1, SquareFreeQ[#]&&And@@PrimePowerQ/@PrimePi/@DeleteCases[FactorInteger[#][[All, 1]], 2]]&]

PROG

(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

CROSSREFS

Cf. A000961, A001222, A003963, A005117, A007716, A056239, A275024, A279786, A281113, A296131, A301767, A302242, A302243, A302493, A302494.

Sequence in context: A246867 A028805 A322846 * A117344 A117204 A129127

Adjacent sequences:  A302493 A302494 A302495 * A302497 A302498 A302499

KEYWORD

nonn

AUTHOR

Gus Wiseman, Apr 09 2018

STATUS

approved

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Last modified July 31 06:14 EDT 2021. Contains 346368 sequences. (Running on oeis4.)