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 A191969 Numbers that are indices of deficient oblong numbers (A002378). 1
 1, 10, 13, 22, 37, 43, 46, 52, 58, 61, 67, 73, 82, 85, 94, 97, 106, 109, 118, 121, 130, 133, 136, 142, 145, 148, 151, 157, 163, 166, 172, 178, 181, 190, 193, 202, 205, 211, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS n such that A002378(n)=n*(n+1) is deficient. "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 O(1100) 17.6% of the oblong numbers are deficient.  The per 100 count of deficient oblong numbers from O(1) to O(1100) is 16, 19, 19, 16, 17, 20, 18, 17, 17, 15, 20. For most deficient oblong numbers in this range either n or n+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. REFERENCES Tattersall, J. "Elementary Number Theory in Nine Chapters", Second Edition, Cambridge University Press, 2005. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 EXAMPLE The third deficient oblong number is A002378(13)=13*14=182. Sigma(182)=336<(2*182). MATHEMATICA Select[Range[400], DivisorSigma[1, o = # (# + 1)] < 2 o &] (* Amiram Eldar, Jun 21 2019 *) PROG (PARI) for(n=1, 400, o=n*(n+1); if(sigma(o)<2*o, print1(n, ", "))) CROSSREFS Cf. A005101, A005100, A002378, A124672, A077804. Equals A077804/(n+1) Sequence in context: A159839 A129075 A095918 * A018785 A176762 A001273 Adjacent sequences:  A191966 A191967 A191968 * A191970 A191971 A191972 KEYWORD easy,nonn AUTHOR Chris Fry, Jun 22 2011 STATUS approved

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Last modified May 28 16:37 EDT 2022. Contains 354119 sequences. (Running on oeis4.)