A102836 Composite numbers whose exponents in their canonical factorization lie in the geometric progression 1, 2, 4, ...

18, 50, 75, 98, 147, 242, 245, 338, 363, 507, 578, 605, 722, 845, 847, 867, 1058, 1083, 1183, 1445, 1587, 1682, 1805, 1859, 1922, 2023, 2523, 2527, 2645, 2738, 2883, 3179, 3362, 3698, 3703, 3757, 3971, 4107, 4205, 4418, 4693, 4805, 5043, 5547, 5618, 5819

Offset

1,1

Comments

The first term not in A095990 is a(70) = 11250.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

Canonical factorization of a(70) = 11250 = 2^1 * 3^2 * 5*4 or 2,3,5 raised to powers 1,2,4 which is a geometric progression.

Mathematica

q[n_] := Module[{e = FactorInteger[n][[;; , 2]]}, Length[e] > 1 && e == 2^Range[0, Length[e]-1]]; Select[Range[6000], q] (* Amiram Eldar, Jun 29 2024 *)

Prog

(PARI) /* Numbers whose factors are primes to perfect powers in a geometric progression. */ 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]==2^(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] != 2^(i-1), return(0))); 1); \\ Amiram Eldar, Jun 29 2024

Crossrefs

Cf. A095990, A102838.

Sequence in context: A089219 A102835 A095990 * A217750 A180292 A143928

Adjacent sequences: A102833 A102834 A102835 * A102837 A102838 A102839

Keyword

easy,nonn

Author

Cino Hilliard, Feb 27 2005

Status

approved