A077804 Deficient oblong numbers.

2, 110, 182, 506, 1406, 1892, 2162, 2756, 3422, 3782, 4556, 5402, 6806, 7310, 8930, 9506, 11342, 11990, 14042, 14762, 17030, 17822, 18632, 20306, 21170, 22052, 22952, 24806, 26732, 27722, 29756, 31862, 32942, 36290, 37442, 41006, 42230

Offset: 1

Author

Jason Earls, Dec 03 2002

Keywords

• easy
• nonn

Comments

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

References

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1001 from Harvey P. Dale)
• Charles de Neuveglise, Traité methodique et abregé de toutes les mathématiques, tome 2 (L’arithmétique ou Science des nombres), Trevoux, 1700, pp. 244-246.
• Leonard Eugene Dickson, History of the Theory of Numbers, Washington, Carnegie Institution of Washington, 1919, p. 15.

Crossrefs

Intersection of A002378 and A005100.

Cf. A005101, A191969.

Programs

Mathematica

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

PARI

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

Formula

a(n) = A002378(A191969(n)). - Amiram Eldar, Mar 11 2024

Extensions

Offset corrected by Amiram Eldar, Mar 11 2024