

A113544


Numbers simultaneously pentagonfree, squarefree and trianglefree.


2



1, 2, 7, 11, 13, 14, 17, 19, 23, 26, 29, 31, 34, 37, 38, 41, 43, 46, 47, 53, 58, 59, 61, 62, 67, 71, 73, 74, 77, 79, 82, 83, 86, 89, 94, 97, 101, 103, 106, 107, 109, 113, 118, 119, 122, 127, 131, 133, 134, 137, 139, 142, 143, 146, 149, 151, 157, 158, 161, 163
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OFFSET

1,2


REFERENCES

Bellman, R. and Shapiro, H. N. "The Distribution of Squarefree Integers in Small Intervals." Duke Math. J. 21, 629637, 1954.
Borwein, J. and Bailey, D. Mathematics by Experiment: Plausible Reasoning in the 21st Century. Natick, MA: A. K. Peters, 2003.
Hardy, G. H. and Wright, E. M. "The Number of Squarefree Numbers." Section 18.6 in An Introduction to the Theory of Numbers, 5th ed. Oxford, England: Clarendon Press, pp. 269270, 1979.


LINKS

G. C. Greubel and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 1000 terms from Greubel)
Eric Weisstein's World of Mathematics, Squarefree.


FORMULA

a(n) has no factor >1 of form a*(a+1)/2 nor b^2 nor c*(3*c1)/2. A005117 INTERSECTION A112886 INTERSECTION A113508.


MATHEMATICA

bad = Rest@ Union[# (# + 1)/2 &@ Range[19], Range[14]^2, # (3 #  1)/2 &@ Range[11]]; Select[Range[200], {} == Intersection[bad, Divisors[#]] &] (* Giovanni Resta, Jun 13 2016 *)


PROG

(PARI) list(lim)=my(v=List()); forsquarefree(n=1, lim\1, fordiv(n, d, if((ispolygonal(d, 3)  ispolygonal(d, 5)) && d>1, next(2))); listput(v, n[1])); Vec(v); \\ Charles R Greathouse IV, Dec 24 2018


CROSSREFS

Cf. A000217, A005117, A113502, A013929, A046098, A059956, A065474, A071172, A087618, A088454, A112886, A113508.
Sequence in context: A184792 A136998 A136734 * A045173 A230048 A201362
Adjacent sequences: A113541 A113542 A113543 * A113545 A113546 A113547


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, Jan 13 2006


EXTENSIONS

Corrected and extended by Giovanni Resta, Jun 13 2016


STATUS

approved



