A346072 Numbers m such that there exist positive integers i < m and j > m such that m = Sum_{k=i..m-1} tau(k) and m = Sum_{k=m+1..j} tau(k), where tau(k) = number of divisors of k = A000005(k).

3, 16, 21, 36, 45, 57, 69, 77, 95, 99, 100, 133, 139, 141, 185, 217, 247, 271, 349, 812, 834, 882, 884, 1012, 1018, 1078, 1138, 1198, 1256, 1404, 1478, 1936, 1985, 2263, 2345, 2381, 2477, 2489, 2549, 2583, 2631, 2847, 2855, 2857, 2865, 2887, 2903, 2947, 2969, 2977, 3005, 3011, 3023, 3028

Offset

1,1

Comments

The terms show a wavelike growth pattern as n increases. See the linked image.

Links

Scott R. Shannon, Table of n, a(n) for n = 1..5000.

Scott R. Shannon, Image of the first 5000 terms.

Example

3 is a term as tau(1) + tau(2) = 1 + 2 = 3, and tau(4) = 3.
16 is a term as tau(12) + tau(13) + tau(14) + tau(15) = 6 + 2 + 4 + 4 = 16 and tau(17) + tau(18) + tau(19) + tau(20) = 2 + 6 + 2 + 6 = 16.
21 is a term as tau(16) + ... + tau(20) = 5 + 2 + 6 + 2 + 6 = 21 and tau(22) + ... tau(26) = 4 + 2 + 8 + 3 + 4 = 21.

Crossrefs

Cf. A000005, A000203, A006218.

Sequence in context: A277724 A175285 A031071 * A218625 A028687 A201274

Adjacent sequences: A346069 A346070 A346071 * A346073 A346074 A346075

Keyword

nonn

Author

Scott R. Shannon, Jul 04 2021

Status

approved