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%I #12 Jun 29 2024 07:17:10
%S 18,50,75,98,147,242,245,338,363,507,578,605,722,845,847,867,1058,
%T 1083,1183,1445,1587,1682,1805,1859,1922,2023,2523,2527,2645,2738,
%U 2883,3179,3362,3698,3703,3757,3971,4107,4205,4418,4693,4805,5043,5547,5618,5819
%N Composite numbers whose exponents in their canonical factorization lie in the geometric progression 1, 2, 4, ...
%C The first term not in A095990 is a(70) = 11250.
%H Amiram Eldar, <a href="/A102836/b102836.txt">Table of n, a(n) for n = 1..10000</a>
%e 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.
%t 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 *)
%o (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",")) ) }
%o (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
%Y Cf. A095990, A102838.
%K easy,nonn
%O 1,1
%A _Cino Hilliard_, Feb 27 2005
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