

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
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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



