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A079431 Least m>n with same smallest odd prime factor as n.

%I A079431 #11 Mar 09 2019 11:32:12
%S A079431 2,4,6,8,10,9,14,16,12,20,22,15,26,28,18,32,34,21,38,25,24,44,46,27,
%T A079431 35,52,30,49,58,33,62,64,36,68,40,39,74,76,42,50,82,45,86,88,48,92,94,
%U A079431 51,56,55,54,104,106,57,65,77,60,116,118,63,122,124,66,128,70,69,134,136
%N A079431 Least m>n with same smallest odd prime factor as n.
%C A079431 A078701(a(n))=A078701(n), A078701(i)<>A078701(n), n<i<a(n);
%C A079431 n + A078701(n) <= a(n) <= 2*n;
%C A079431 a(2^k) = 2^(k+1), as A078701(2^k) = 1.
%H A079431 Robert Israel, <a href="/A079431/b079431.txt">Table of n, a(n) for n = 1..10000</a>
%p A079431 N:= 100:
%p A079431 A:= Vector(N):
%p A079431 p:= 2:
%p A079431 do
%p A079431   p:= nextprime(p);
%p A079431   if p > N then break fi;
%p A079431   R:= select(k -> A[k] = 0, [$1..N]);
%p A079431   S:= select(`<=`,R,N/p);
%p A079431   A[p*S]:= Vector(p*R[2..1+nops(S)]);
%p A079431 od:
%p A079431 for k from 0 to ilog2(N) do A[2^k]:= 2^(k+1) od:
%p A079431 convert(A,list); # _Robert Israel_, Oct 25 2017
%t A079431 sopf[n_] := SelectFirst[FactorInteger[n][[All, 1]], # > 2&];
%t A079431 a[n_] := For[p = sopf[n]; m = n+1, True, m++, If[p == sopf[m], Return[m]]];
%t A079431 Array[a, 100] (* _Jean-François Alcover_, Mar 09 2019 *)
%Y A079431 Cf. A079432(n) = a(a(n)).
%Y A079431 Cf. A078701.
%K A079431 nonn,look
%O A079431 1,1
%A A079431 _Reinhard Zumkeller_, Jan 09 2003