This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A191969 #30 Mar 15 2024 05:51:22 %S A191969 1,10,13,22,37,43,46,52,58,61,67,73,82,85,94,97,106,109,118,121,130, %T A191969 133,136,142,145,148,151,157,163,166,172,178,181,190,193,202,205,211, %U A191969 214,217,226,229,232,238,241,250,253,262,268,277,283,289,292,298,301,310,313,316,322,331,334,337,346,358,361,373,382,388,394,397 %N A191969 Numbers that are indices of deficient oblong numbers (A002378). %C A191969 Numbers k such that A002378(k) = k*(k+1) is deficient. %C A191969 "In 1700, Charles de Neuveglise claimed the product of two consecutive integers n(n+1) with n>=3 is abundant." - Tattersall, p. 144. In other words, de Neuveglise claimed that all oblong numbers greater than 6 are abundant. In fact, up to A002378(1100), 17.6% of the oblong numbers are deficient. The per-100 count of deficient oblong numbers from A002378(1) to A002378(1100) is 16, 19, 19, 16, 17, 20, 18, 17, 17, 15, 20. For most deficient oblong numbers A002378(k) in this range, either k or k+1 is prime, but this is not always the case, explaining why the density of deficient oblong numbers does not decrease in line with the primes. %C A191969 All the terms are congruent to 1 or 4 mod 6, and there are no terms that are congruent to 0, 4, 15, or 19 mod 20. Therefore, the asymptotic density of this sequence is less than 4/15. The numbers of terms that do not exceed 10^k, for k = 1, 2, ..., are 2, 16, 174, 1831, 18237, 182432, 1824453, 18241059, 182414767, 1824169736, ... . Apparently, the asymptotic density of this sequence equals 0.18241... . - _Amiram Eldar_, Mar 15 2024 %D A191969 James J. Tattersall, Elementary Number Theory in Nine Chapters, Second Edition, Cambridge University Press, 2005. %H A191969 Amiram Eldar, <a href="/A191969/b191969.txt">Table of n, a(n) for n = 1..10000</a> %F A191969 A002378(a(n)) = A077804(n). - _Amiram Eldar_, Mar 15 2024 %e A191969 The third deficient oblong number is A002378(13) = 13*14 = 182: sigma(182) = 336 < 364 = 2*182. %t A191969 Select[Range[400], DivisorSigma[1, o = # (# + 1)] < 2 o &] (* _Amiram Eldar_, Jun 21 2019 *) %o A191969 (PARI) for(n=1, 400, o=n*(n+1); if(sigma(o)<2*o, print1(n, ", "))) %Y A191969 Cf. A005101, A005100, A002378, A124672, A077804. %K A191969 easy,nonn %O A191969 1,2 %A A191969 _Chris Fry_, Jun 22 2011