A102835 Composite numbers whose exponents in their canonical factorization are an initial segment of the positive integers.

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, 2250, 2523, 2527, 2645, 2738, 2883, 3179, 3362, 3698, 3703, 3757, 3971, 4107, 4205, 4418, 4693, 4805, 5043, 5547, 5618

Offset

1,1

Comments

Differs from A095990 starting with the number 2250.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

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

Maple

filter:= proc(n) local F, m, i;
  F:= map(t->t[2], sort(ifactors(n)[2], (a, b) -> a[1]<b[1]));
  nops(F) > 1 and F = [$1..nops(F)]
end proc:
select(filter, [$2..10^4]); # Robert Israel, Nov 23 2016

Mathematica

filterQ[n_] := CompositeQ[n] && With[{f = FactorInteger[n][[All, 2]]}, f == Range[Length[f]]];
Select[Range[10000], filterQ] (* Jean-François Alcover, Aug 28 2020 *)

Prog

(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", ")) ) }

Crossrefs

Cf. A095990.

Sequence in context: A354929 A093617 A089219 * A095990 A102836 A217750

Adjacent sequences: A102832 A102833 A102834 * A102836 A102837 A102838

Keyword

easy,nonn

Author

Cino Hilliard, Feb 27 2005

Extensions

Name changed by Robert Israel, Nov 23 2016

Status

approved