A266115 Numbers which have smaller siblings in A263267-tree: numbers n for which there exists some k < n such that k - d(k) = n - d(n), where d(n) = A000005(n), the number of divisors of n.

2, 4, 10, 12, 15, 16, 21, 26, 28, 30, 33, 36, 39, 42, 45, 48, 52, 54, 55, 60, 63, 64, 66, 69, 70, 75, 76, 78, 80, 85, 90, 91, 100, 108, 110, 111, 112, 115, 117, 122, 124, 126, 129, 132, 133, 138, 140, 141, 144, 147, 148, 150, 153, 156, 159, 165, 168, 170, 171, 172, 174, 176, 180, 182, 183, 189, 190, 192, 196, 201, 207, 208, 213, 222

Offset

1,1

Comments

At least initially, the majority of the odd squares (A016754) seem to be in A266114, while the majority of the even squares (A016742) seem to be in A266115. The first exceptions to this are 63^2 = 3969 = A266115(1296), and 20^2 = 400 = A266114(269).

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Example

2 is present, as 2 - A000005(2) = 0, but also 1 - A000005(1) = 0, thus 1 is a smaller sibling of 2 in a tree A263267 defined by edge-relation child - A000005(child) = parent.

Prog

(Scheme, with Antti Karttunen's IntSeq-library)
(define A266115 (ZERO-POS 1 1 A266112))

Crossrefs

Cf. A000005, A082284, A263267, A266112.

Cf. A266114 (complement).

Sequence in context: A138940 A278465 A129412 * A113536 A081887 A085344

Adjacent sequences: A266112 A266113 A266114 * A266116 A266117 A266118

Keyword

nonn

Author

Antti Karttunen, Dec 21 2015

Status

approved