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
Examples
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.
Links
- Alois P. Heinz, Table of n, a(n) for n = 1..10000
- Alec Jones, Java program
Programs
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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 *) -
PARI
isok(n)=my(f = factor(n)); for (k=1, #f~, if (isprime(f[k,2]), return (0));); 1; \\ Michel Marcus, Jun 07 2016
Comments