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A102835
Composite numbers whose exponents in their canonical factorization are an initial segment of the positive integers.
1
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
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
KEYWORD
easy,nonn
AUTHOR
Cino Hilliard, Feb 27 2005
EXTENSIONS
Name changed by Robert Israel, Nov 23 2016
STATUS
approved