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

5, 23, 44, 84, 132, 185, 335, 368, 1342, 2226, 3354, 4726, 7359, 7598, 8436, 10234, 12123, 18078, 18744, 19848, 20492, 20922, 21823, 21902, 23218, 24069, 24221, 31678, 36510, 36849, 40235, 45046, 46916, 49356, 49769, 50560, 51780, 52716, 53079, 59942, 60150

Offset: 1

Author

Paolo P. Lava, Feb 13 2013

Keywords

• nonn

Comments

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):

sigma#(n)=sigma#(n+1).

Examples

			n=44; sigma#(44)=18 and sigma#(45)=18.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A000961, A001358, A003418, A005179, A024619, A034444, A077610, A222084, A222085.

Programs

Maple

with(numtheory);
A222088:=proc(q)
local a,b,c,d,j,n,t,v;
d:=1;
for n from 2 to q do
  a:=ifactors(n)[2]; b:=nops(a); c:=0; v:=0;
  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;
  a:=op(sort([op(divisors(n))])); b:=nops(divisors(n));
  for j from 1 to b do v:=v+a[j]; if a[j]=c then break; fi; od;
  if d=v then print(n-1); fi; d:=v; od; end:
A222088(1000000);

Mathematica

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 *)