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

1,1

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A102836.

Sequence in context: A221867 A248209 A245830 * A090832 A232511 A262853

Adjacent sequences: A102835 A102836 A102837 * A102839 A102840 A102841

Keyword

easy,nonn

Author

Cino Hilliard, Feb 27 2005

Status

approved