A102838 Composite numbers whose exponents in their canonical factorization lie in the geometric progression 1, 3, 9, ...

54, 250, 375, 686, 1029, 1715, 2662, 3993, 4394, 6591, 6655, 9317, 9826, 10985, 13718, 14739, 15379, 20577, 24167, 24334, 24565, 34295, 34391, 36501, 48013, 48778, 54043, 59582, 60835, 63869, 73167, 75449, 85169, 89167, 89373

Offset: 1

Author

Cino Hilliard, Feb 27 2005

Keywords

• easy
• nonn

Examples

			The first term having more than 2 prime powers is 105468750 = 2^1 * 3^3 * 5^9, not shown.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..3000

Crossrefs

Cf. A102836.

Programs

Mathematica

q[n_] := Module[{e = FactorInteger[n][[;;, 2]]}, Length[e] > 1 && e == 3^Range[0, Length[e]-1]]; Select[Range[10^5], q] (* Amiram Eldar, Jun 29 2024 *)

PARI

geoprog(n,m) = { local(a,x,j,nf,fl=0); for(x=1,n, a=factor(x); nf=omega(x); for(j=1,nf, if(a[j,2]==3^(j-1),fl=1,fl=0;break); ); if(fl&nf>1,print1(x",")) ) }

PARI

is(n) = if(n == 1 || isprime(n), 0, my(e = factor(n)[, 2]); for(i = 1, #e, if(e[i] != 3^(i-1), return(0))); 1); \\ Amiram Eldar, Jun 29 2024