cp's OEIS Frontend

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.

%I A266114 #16 Dec 23 2015 14:11:40
%S A266114 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,
%T A266114 38,40,41,43,44,46,47,49,50,51,53,56,57,58,59,61,62,65,67,68,71,72,73,
%U A266114 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
%N 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.
%C A266114 Sequence A082284 sorted into ascending order, with zeros removed.
%C A266114 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).
%H A266114 Antti Karttunen, <a href="/A266114/b266114.txt">Table of n, a(n) for n = 1..10000</a>
%F A266114 Other identities. For all n >= 1:
%F A266114 A266113(a(n)) = n.
%e A266114 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.
%o A266114 (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o A266114 (define A266114 (NONZERO-POS 1 1 A266112))
%Y A266114 Cf. A000005, A082284, A263267.
%Y A266114 Cf. A266112 (characteristic function).
%Y A266114 Cf. A266113 (least monotonic left inverse).
%Y A266114 Cf. A266115 (complement).
%Y A266114 Cf. A065091, A261089, A264988, A262509 (subsequences).
%Y A266114 Cf. also A016742, A016754.
%K A266114 nonn
%O A266114 1,2
%A A266114 _Antti Karttunen_, Dec 21 2015