A266114 Least siblings in A263267-tree: numbers n for which there doesn't exist any k < n such that k - d(k) = n - d(n), where d(n) = A000005(n), the number of divisors of n.

1, 3, 5, 6, 7, 8, 9, 11, 13, 14, 17, 18, 19, 20, 22, 23, 24, 25, 27, 29, 31, 32, 34, 35, 37, 38, 40, 41, 43, 44, 46, 47, 49, 50, 51, 53, 56, 57, 58, 59, 61, 62, 65, 67, 68, 71, 72, 73, 74, 77, 79, 81, 82, 83, 84, 86, 87, 88, 89, 92, 93, 94, 95, 96, 97, 98, 99, 101, 102, 103, 104, 105, 106, 107, 109, 113, 114, 116, 118, 119, 120, 121, 123, 125, 127, 128

Offset: 1

Author

Antti Karttunen, Dec 21 2015

Keywords

• nonn

Comments

Sequence A082284 sorted into ascending order, with zeros removed.

At least initially, most of the odd squares (A016754) seem to be in A266114, while most 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).

Examples

			3 is present, as 3 - A000005(3) = 1, but there are no any number k less than 3 for which k - A000005(k) = 1. (Although there is a larger sibling 4, for which 4 - A000005(4) = 1 also). Thus 3 is a smallest children of 1 in a tree A263267 defined by edge-relation child - A000005(child) = parent.
		

Links

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

Crossrefs

Cf. A000005, A082284, A263267.

Cf. A266112 (characteristic function).

Cf. A266113 (least monotonic left inverse).

Cf. A266115 (complement).

Cf. A065091, A261089, A264988, A262509 (subsequences).

Cf. also A016742, A016754.

Formula

Other identities. For all n >= 1:

A266113(a(n)) = n.