

A187204


Numbers n such that the bottom entry in the difference table of the divisors of n is 0.


9




OFFSET

1,1


COMMENTS

Numbers n such that A187202(n) = 0.
11373118351 and 1756410942451 are also in the sequence (not necessarily the next two terms).  Donovan Johnson, Aug 05 2011
For every integer m, does there exist a prime p such that abs(A187202(r * m)) > abs(A187202(q * m)) and sign(A187202(r * m)) = sign(A187202(q * m)), and q >= p is prime and prime r > q?  David A. Corneth, Apr 08 2017
No other terms up to 3*10^9.  Michel Marcus, Apr 09 2017
a(9) > 6*10^10. 138662735650982521 and 168248347462416481 are also terms.  Giovanni Resta, Apr 12 2017


LINKS

Table of n, a(n) for n=1..8.


EXAMPLE

10 has divisors 1, 2, 5, 10. The third difference of these numbers is 0. This is the only possible number having 2 prime factors of the form p*q. The other terms have factorization 171 = 3^2*19, 1947 = 3*11*59, 2619 = 3^3*97, and 265105 = 5*37*1433.


MATHEMATICA

t = {}; Do[d = Divisors[n]; If[Differences[d, Length[d]1] == {0}, AppendTo[t, n]], {n, 10^4}]; t (* T. D. Noe, Aug 01 2011 *)


PROG

(Haskell)
import Data.List (elemIndices)
a187204 n = a187204_list !! (n1)
a187204_list = map (+ 1) $ elemIndices 0 $ map a187202 [1..]
 Reinhard Zumkeller, Aug 02 2011
(PARI) is(n) = my(d=divisors(n)); !sum(i=1, #d, binomial(#d1, i1)*d[i]*(1)^i) \\ David A. Corneth, Apr 08 2017


CROSSREFS

Cf. A027750, A187202, A187203, A193671, A193672.
Sequence in context: A034830 A098345 A119043 * A133273 A239763 A112703
Adjacent sequences: A187201 A187202 A187203 * A187205 A187206 A187207


KEYWORD

nonn,more,hard


AUTHOR

Omar E. Pol, Aug 01 2011


EXTENSIONS

Suggested by T. D. Noe in the "history" of A187203.
a(6)a(7) from Donovan Johnson, Aug 03 2011
a(8) from Giovanni Resta, Apr 11 2017


STATUS

approved



