

A274034


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


2



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
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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(n1)+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: A336222 A252895 A336224 * A197680 A119024 A321453
Adjacent sequences: A274031 A274032 A274033 * A274035 A274036 A274037


KEYWORD

nonn,easy


AUTHOR

Alec Jones, Jun 07 2016


STATUS

approved



