

A181568


Numbers k such that the largest prime factor of k^21 is 101.


25



100, 201, 203, 302, 304, 403, 405, 506, 607, 706, 807, 809, 1009, 1011, 1112, 1211, 1312, 1415, 1514, 1516, 1716, 1819, 1918, 2221, 2324, 2524, 2526, 2625, 2627, 3231, 3233, 3334, 3433, 3635, 3736, 3839, 4041, 4241, 4344, 4445, 4544, 4645, 4647, 4746
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Sequence is finite, number of terms and last term are still unknown (cf. A175607, A181471).
From David A. Corneth, Sep 11 2019: (Start)
Are there any terms > 941747621709311?
As k^2  1 = (k  1)(k + 1), a(n) is of the form 101*m + 1. (End)


LINKS

David A. Corneth, Table of n, a(n) for n = 1..3340 (first 2325 terms from Klaus Brockhaus, terms < 10^17).
Florian Luca, Filip Najman, On the largest prime factor of x^21, arXiv:1005.1533 [math.NT], 2010.
Florian Luca, Filip Najman, On the largest prime factor of x^21, Mathematics of Computation 80 (2011), 429435. (Paper has errata that was posted on the MOC website.)


MATHEMATICA

Select[Range[4746], FactorInteger[#^21][[1, 1]]==101&] (* Metin Sariyar, Sep 15 2019 *)


PROG

(MAGMA) [ n: n in [2..5000]  m eq 101 where m is D[#D] where D is PrimeDivisors(n^21) ];
(PARI) is(n)=n=n^21; forprime(p=2, 97, n/=p^valuation(n, p)); n>1 && 101^valuation(n, 101)==n \\ Charles R Greathouse IV, Jul 01 2013


CROSSREFS

Cf. A175607, A181471, A181447A181470.
Sequence in context: A322835 A031498 A053402 * A308306 A235272 A249702
Adjacent sequences: A181565 A181566 A181567 * A181569 A181570 A181571


KEYWORD

fini,nonn


AUTHOR

Klaus Brockhaus, Oct 31 2010


STATUS

approved



