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).

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, 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, 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

Offset

1,3

Comments

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.

Links

Table of n, a(n) for n=1..94.

Scott R. Shannon, Image of the first 2000000 terms.

Example

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.

Prog

(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

Crossrefs

Cf. A000203, A276457, A356348.

Sequence in context: A133622 A158416 A318225 * A335497 A309872 A359031

Adjacent sequences: A360254 A360255 A360256 * A360258 A360259 A360260

Keyword

nonn

Author

Scott R. Shannon, Jan 31 2023

Status

approved