A187204 Numbers n such that the bottom entry in the difference table of the divisors of n is 0.

10, 171, 1947, 2619, 265105, 478834027, 974622397, 11373118351

Offset: 1

Author

Omar E. Pol, Aug 01 2011

Keywords

• nonn
• more
• hard

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

Examples

			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.
		

Crossrefs

Cf. A027750, A187202, A187203, A193671, A193672.

Programs

Haskell

import Data.List (elemIndices)
a187204 n = a187204_list !! (n-1)
a187204_list = map (+ 1) $ elemIndices 0 $ map a187202 [1..]
-- Reinhard Zumkeller, Aug 02 2011

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 *)

PARI

is(n) = my(d=divisors(n)); !sum(i=1, #d, binomial(#d-1,i-1)*d[i]*(-1)^i) \\ David A. Corneth, Apr 08 2017

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