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
Examples
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.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
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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 *) -
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
Comments