A226648 Numbers k such that Sum_{j=1..k} sigma(j) is a triangular number, where sigma(j) = sum of divisors of j (A000203).

1, 4, 5, 50, 64, 906, 966, 5805, 40514, 133667, 262277, 1416109, 42142704, 189758142, 350476553, 957982453, 1420733777, 1421477786, 2557347701, 28609375750, 95023678204, 100094778026, 119964793932

Offset

1,2

Comments

Indices of triangular numbers in A024916.

The sequence of indices of generated triangular numbers b(n) begins: 1, 5, 6, 64, 82, 1162, 1239, 7445, 51961, 171434, 336383, 1816230, 54050118, 243374273, 449503643, 1228660232, 1822161864, 1823116093, 3279925859. A024916(a(n)) = A000217(b(n)).

Links

Table of n, a(n) for n=1..23.

Lucas A. Brown, Python program.

Prog

(PARI) isok(n) = ispolygonal(sum(k=1, n, sigma(k)), 3); \\ Michel Marcus, Nov 08 2014
(Python) # See LINKS.

Crossrefs

Cf. A000203, A000217, A024916, A130698.

Sequence in context: A151486 A042383 A135799 * A335797 A041941 A220534

Adjacent sequences: A226645 A226646 A226647 * A226649 A226650 A226651

Keyword

nonn,more,hard

Author

Alex Ratushnyak, Jun 13 2013

Extensions

a(20)-a(23) from Lucas A. Brown, Mar 08 2024

Status

approved