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
KEYWORD
easy,nonn
AUTHOR
Cino Hilliard, Feb 27 2005
STATUS
approved