

A117583


For successive primes p, the number of ratios t(n)/(t(n)1), where t(n)=n(n+1)/2 is the nth triangular number, which factor into primes less than or equal to p.


2



0, 1, 3, 7, 9, 16, 22, 29, 35, 39, 50, 57, 68
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,3


COMMENTS

As in the case of square numerators, triangular numerators of superparticular ratios m/(m1) factorizable only up to a relatively small prime p are relatively common.


REFERENCES

E. F. Ecklund and R. B. Eggleton, Prime factors of consecutive integers, Amer. Math. Monthly, 79 (1972), 10821089.
D. H. Lehmer, On a problem of Stormer, Ill. J. Math., 8 (1964), 5769.


LINKS

Table of n, a(n) for n=1..13.


CROSSREFS

Cf. A002071, A117582.
Sequence in context: A192118 A057463 A118258 * A126106 A064194 A036978
Adjacent sequences: A117580 A117581 A117582 * A117584 A117585 A117586


KEYWORD

hard,nonn


AUTHOR

Gene Ward Smith, Apr 02 2006


STATUS

approved



