A274034 Numbers whose exponents in their prime power factorizations are not primes.

1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 26, 29, 30, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 46, 47, 48, 51, 53, 55, 57, 58, 59, 61, 62, 64, 65, 66, 67, 69, 70, 71, 73, 74, 77, 78, 79, 80, 81, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97

Offset

1,2

Comments

The density of this sequence is 0.6504456084..., see A273487. - Charles R Greathouse IV, Jul 01 2016

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Alec Jones, Java program

Example

8 is not present in this sequence because 8 = 2^3 and 3 is prime.
96 is not present in this sequence because 96 = 2^5*3^1 and 5 is prime.

Maple

a:= proc(n) option remember; local k; for k from
      `if`(n=1, 1, a(n-1)+1) while ormap(i->
       isprime(i[2]), ifactors(k)[2]) do od; k
    end:
seq(a(n), n=1..80);  # Alois P. Heinz, Jun 30 2016

Mathematica

lst0={}; Do[lst[n]=Transpose[FactorInteger[n]][[2]]; k=1; While[!(PrimeQ[lst[n][[k]]]||k==Length[lst[n]]), k++]; If[k==Length[lst[n]]&&!PrimeQ[Last[lst[n]]], AppendTo[lst0, n]], {n, 91}]; lst0 (* Waldemar Puszkarz, Jun 09 2016 *)

Prog

(PARI) isok(n)=my(f = factor(n)); for (k=1, #f~, if (isprime(f[k, 2]), return (0)); ); 1; \\ Michel Marcus, Jun 07 2016

Crossrefs

Cf. A056166 (exponents are prime), A197680 (exponents are squares).

Sequence in context: A252895 A366242 A336224 * A197680 A361177 A366762

Adjacent sequences: A274031 A274032 A274033 * A274035 A274036 A274037

Keyword

nonn,easy

Author

Alec Jones, Jun 07 2016

Status

approved