A102835 - OEIS

%I #15 Aug 28 2020 03:25:22

%S 18,50,75,98,147,242,245,338,363,507,578,605,722,845,847,867,1058,

%T 1083,1183,1445,1587,1682,1805,1859,1922,2023,2250,2523,2527,2645,

%U 2738,2883,3179,3362,3698,3703,3757,3971,4107,4205,4418,4693,4805,5043,5547,5618

%N Composite numbers whose exponents in their canonical factorization are an initial segment of the positive integers.

%C Differs from A095990 starting with the number 2250.

%H Robert Israel, <a href="/A102835/b102835.txt">Table of n, a(n) for n = 1..10000</a>

%e Canonical factorization of 2250 = 2^1 * 3^2 * 5^3 or 2,3,5 raised to powers 1,2,3, an arithmetic progression.

%p filter:= proc(n) local F,m,i;

%p   F:= map(t->t[2],sort(ifactors(n)[2],(a,b) -> a[1]<b[1]));

%p   nops(F) > 1 and F = [$1..nops(F)]

%p end proc:

%p select(filter, [$2..10^4]); # _Robert Israel_, Nov 23 2016

%t filterQ[n_] := CompositeQ[n] && With[{f = FactorInteger[n][[All, 2]]}, f == Range[Length[f]]];

%t Select[Range[10000], filterQ] (* _Jean-François Alcover_, Aug 28 2020 *)

%o (PARI) omnipprog(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]==j,fl=1,fl=0;break); ); if(fl&nf>1,print1(x",")) ) }

%Y Cf. A095990.

%K easy,nonn

%O 1,1

%A _Cino Hilliard_, Feb 27 2005

%E Name changed by _Robert Israel_, Nov 23 2016