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A222088 Numbers n for which A222085(n)=A222085(n+1).

%I A222088 #17 Jun 02 2025 08:24:06
%S A222088 5,23,44,84,132,185,335,368,1342,2226,3354,4726,7359,7598,8436,10234,
%T A222088 12123,18078,18744,19848,20492,20922,21823,21902,23218,24069,24221,
%U A222088 31678,36510,36849,40235,45046,46916,49356,49769,50560,51780,52716,53079,59942,60150
%N A222088 Numbers n for which A222085(n)=A222085(n+1).
%C A222088 Like A002961 but using sigma#(n), sum of the least divisors of n whose LCM is equal to n, as defined in A222085, instead of sigma(n):
%C A222088 sigma#(n)=sigma#(n+1).
%H A222088 Amiram Eldar, <a href="/A222088/b222088.txt">Table of n, a(n) for n = 1..10000</a>
%e A222088 n=44; sigma#(44)=18 and sigma#(45)=18.
%p A222088 with(numtheory);
%p A222088 A222088:=proc(q)
%p A222088 local a,b,c,d,j,n,t,v;
%p A222088 d:=1;
%p A222088 for n from 2 to q do
%p A222088   a:=ifactors(n)[2]; b:=nops(a); c:=0; v:=0;
%p A222088   for j from 1 to b do if a[j][1]^a[j][2]>c then c:=a[j][1]^a[j][2]; fi; od;
%p A222088   a:=op(sort([op(divisors(n))])); b:=nops(divisors(n));
%p A222088   for j from 1 to b do v:=v+a[j]; if a[j]=c then break; fi; od;
%p A222088   if d=v then print(n-1); fi; d:=v; od; end:
%p A222088 A222088(1000000);
%t A222088 s[n_] := Module[{sum=0, L=1}, Do[sum+=d; L = LCM[L, d]; If[L == n, Break[]], {d, Divisors[n]}]; sum]; s1=1; seq={}; Do[s2=s[n]; If[s1==s2, AppendTo[seq, n-1]]; s1=s2, {n, 2, 10^4}]; seq (* _Amiram Eldar_, Nov 05 2019 *)
%Y A222088 Cf. A000005, A000961, A001358, A003418, A005179, A024619, A034444, A077610, A222084, A222085.
%K A222088 nonn
%O A222088 1,1
%A A222088 _Paolo P. Lava_, Feb 13 2013