cp's OEIS Frontend

A360257 a(1) = 1; for n > 1, a(n) is the number of preceding terms having the same sum of divisors as a(n-1).

%I A360257 #13 Jan 31 2023 08:21:49
%S A360257 1,1,2,1,3,1,4,1,5,1,6,1,7,1,8,1,9,1,10,1,11,2,2,3,2,4,2,5,2,6,3,3,4,
%T A360257 3,5,3,6,4,4,5,4,6,5,5,6,6,7,2,7,3,7,4,7,5,7,6,8,2,8,3,8,4,8,5,8,6,9,
%U A360257 2,9,3,9,4,9,5,9,6,10,2,10,3,10,4,10,5,10,6,11,12,1,12,2,11,13,1
%N A360257 a(1) = 1; for n > 1, a(n) is the number of preceding terms having the same sum of divisors as a(n-1).
%C A360257 The most common sum of divisor count of all previous terms changes as n increases; these values, up to 2 million terms, are 1, 12, 24, 12, 24, 72, 720, 72, 720, 72, 720, 72, 720. The value 72 holds the record from a(6998) = 71 to a(1271035) = 563. After a(1285242) = 264 the divisor sum 720 becomes the most common sum to well beyond 10 million terms. It is likely the record becomes arbitrarily large as n increases.
%H A360257 Scott R. Shannon, <a href="/A360257/a360257.png">Image of the first 2000000 terms</a>.
%e A360257 a(22) = 2 as a(21) = 11 and 11 has a divisor sum of A000203(11) = 12. However, A000203(6) also equals 12, and as a(11) = 6 there are two previous terms with a divisor sum of 12.
%o A360257 (PARI) lista(nn) = my(va = vector(nn), vs=vector(nn)); va[1] = 1; vs[1] = 1; for (n=2, nn, va[n] = #select(x->(x==vs[n-1]), vs); vs[n] = sigma(va[n]);); va; \\ _Michel Marcus_, Jan 31 2023
%Y A360257 Cf. A000203, A276457, A356348.
%K A360257 nonn
%O A360257 1,3
%A A360257 _Scott R. Shannon_, Jan 31 2023