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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.
5
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
1,2
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).
LINKS
FORMULA
Other identities. For all n >= 1:
A266113(a(n)) = n.
EXAMPLE
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.
PROG
(Scheme, with Antti Karttunen's IntSeq-library)
(define A266114 (NONZERO-POS 1 1 A266112))
CROSSREFS
Cf. A266112 (characteristic function).
Cf. A266113 (least monotonic left inverse).
Cf. A266115 (complement).
Cf. A065091, A261089, A264988, A262509 (subsequences).
Cf. also A016742, A016754.
Sequence in context: A047585 A288224 A039063 * A254130 A114978 A138891
KEYWORD
nonn
AUTHOR
Antti Karttunen, Dec 21 2015
STATUS
approved