cp's OEIS Frontend

A240092 Sequence of numbers starting at 1 and giving a new maximum record for sigma(n) modulo n (A054024), where sigma(n) is the sum of divisors of n (A000203).

%I A240092 #8 Jun 09 2024 10:59:49
%S A240092 1,2,4,8,10,14,16,26,32,44,50,52,60,64,76,92,105,110,128,136,152,170,
%T A240092 184,225,230,232,248,256,296,315,336,376,410,424,470,472,484,512,568,
%U A240092 584,592,630,656,688,752,792,848,884,944,976,988,1012,1024,1072,1136
%N A240092 Sequence of numbers starting at 1 and giving a new maximum record for sigma(n) modulo n (A054024), where sigma(n) is the sum of divisors of n (A000203).
%C A240092 If m is a power of 2, then sigma(m) = 2*m - 1 = m - 1, so sigma(m) == m-1 modulo m, thus giving a new record for A054024, hence A000079 is a subsequence.
%H A240092 Giovanni Resta, <a href="/A240092/b240092.txt">Table of n, a(n) for n = 1..10000</a>
%e A240092 From the first terms of A054024 : 0, 1, 1, 3, 1, 0, 1, 7, 4, 8, 1, 4, 1, 10, ... we can see the records 0, 1, 3, 7, 8, 10, ... obtained for 1, 2, 4, 8, 10, ....
%t A240092 DeleteDuplicates[Table[{n,Mod[DivisorSigma[1,n],n]},{n,1200}],GreaterEqual[#1[[2]],#2[[2]]]&][[;;,1]] (* _Harvey P. Dale_, Jun 09 2024 *)
%o A240092 (PARI) lista(nn) = {rec = -1; for (n=1, nn, sm = sigma(n) % n; if (sm > rec, rec = sm; print1(n, ", ");););}
%Y A240092 Cf. A000079, A000203, A054024.
%K A240092 nonn
%O A240092 1,2
%A A240092 _Michel Marcus_, Apr 01 2014