A289558 Numbers with two distinct prime factors not divisible by a square larger than 4.

6, 10, 12, 14, 15, 20, 21, 22, 24, 26, 28, 33, 34, 35, 38, 39, 40, 44, 46, 48, 51, 52, 55, 56, 57, 58, 62, 65, 68, 69, 74, 76, 77, 80, 82, 85, 86, 87, 88, 91, 92, 93, 94, 95, 96, 104, 106, 111, 112, 115, 116, 118, 119, 122, 123, 124, 129, 133, 134, 136, 141, 142, 143, 145, 146, 148, 152

Offset

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

10 is in this sequence because A001221(10) = 2 and 10 is not divisible by a square greater than 4.

Mathematica

With[{nn = 10^4, r = 2}, Take[#, 67] &@ Union@ Flatten@ Table[Function[p, {p*2^Range[Log2[nn/p]], p DeleteCases[Prime@ Range[r, PrimePi[nn/p]], q_ /; q == p]}]@ Prime@ n, {n, r, PrimePi[nn/Prime[r]]}]] (* Michael De Vlieger, Jul 10 2017 *)

Prog

(PARI) list(lim)=my(v=List()); forprime(p=5, lim\3, forprime(q=3, min(lim\p, p-2), listput(v, p*q))); for(e=1, logint(lim\3, 2), forprime(p=3, lim>>e, listput(v, p<<e))); Set(v) \\ Charles R Greathouse IV, Aug 09 2017

Crossrefs

The union of A046388 and A100368.

Cf. A001221, A007814, A289184.

Sequence in context: A362980 A097318 A080363 * A082300 A050703 A361126

Adjacent sequences: A289555 A289556 A289557 * A289559 A289560 A289561

Keyword

nonn,easy

Author

Juri-Stepan Gerasimov, Jul 08 2017

Status

approved