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Deficient oblong numbers.
3

%I #20 Mar 11 2024 04:22:12

%S 2,110,182,506,1406,1892,2162,2756,3422,3782,4556,5402,6806,7310,8930,

%T 9506,11342,11990,14042,14762,17030,17822,18632,20306,21170,22052,

%U 22952,24806,26732,27722,29756,31862,32942,36290,37442,41006,42230

%N Deficient oblong numbers.

%C "In 1700, Charles de Neuveglise claimed the product of two consecutive integers n(n+1) with n>=3 is abundant." - Tattersall, p. 133.

%D James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 2001.

%H Amiram Eldar, <a href="/A077804/b077804.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1001 from Harvey P. Dale)

%H Charles de Neuveglise, <a href="https://books.google.com/books?id=pmQsF89utUEC&amp;pg=PA244">Traité methodique et abregé de toutes les mathématiques</a>, tome 2 (L’arithmétique ou Science des nombres), Trevoux, 1700, pp. 244-246.

%H Leonard Eugene Dickson, <a href="https://archive.org/details/historyoftheoryo01dick_1/page/15/mode/1up">History of the Theory of Numbers</a>, Washington, Carnegie Institution of Washington, 1919, p. 15.

%F a(n) = A002378(A191969(n)). - _Amiram Eldar_, Mar 11 2024

%t Select[Table[n(n+1),{n,300}],DivisorSigma[1,#]<2#&] (* _Harvey P. Dale_, Oct 03 2011 *)

%o (PARI) for(n=1,350,o=n*(n+1); if(sigma(o)<2*o,print1(o,",")))

%Y Intersection of A002378 and A005100.

%Y Cf. A005101, A191969.

%K easy,nonn

%O 1,1

%A _Jason Earls_, Dec 03 2002

%E Offset corrected by _Amiram Eldar_, Mar 11 2024