A302494 Products of distinct primes of squarefree index.

1, 2, 3, 5, 6, 10, 11, 13, 15, 17, 22, 26, 29, 30, 31, 33, 34, 39, 41, 43, 47, 51, 55, 58, 59, 62, 65, 66, 67, 73, 78, 79, 82, 83, 85, 86, 87, 93, 94, 101, 102, 109, 110, 113, 118, 123, 127, 129, 130, 134, 137, 139, 141, 143, 145, 146, 149, 155, 157, 158, 163

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 set systems.
01: {}
02: {{}}
03: {{1}}
05: {{2}}
06: {{},{1}}
10: {{},{2}}
11: {{3}}
13: {{1,2}}
15: {{1},{2}}
17: {{4}}
22: {{},{3}}
26: {{},{1,2}}
29: {{1,3}}
30: {{},{1},{2}}
31: {{5}}
33: {{1},{3}}
34: {{},{4}}
39: {{1},{1,2}}

Mathematica

Select[Range[100], Or[#===1, SquareFreeQ[#]&&And@@SquareFreeQ/@PrimePi/@FactorInteger[#][[All, 1]]]&]

Prog

(PARI) is(n) = if(bigomega(n)!=omega(n), return(0), my(f=factor(n)[, 1]~); for(k=1, #f, if(!issquarefree(primepi(f[k])) && primepi(f[k])!=1, return(0)))); 1 \\ Felix Fröhlich, Apr 10 2018

Crossrefs

Cf. A000961, A001222, A003963, A005117, A007716, A056239, A270995, A275024, A276625, A277098, A279785, A281113, A296120, A301754, A302242, A302243.

Sequence in context: A034044 A047447 A094739 * A302534 A063451 A276625

Adjacent sequences: A302491 A302492 A302493 * A302495 A302496 A302497

Keyword

nonn

Author

Gus Wiseman, Apr 08 2018

Status

approved