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A187204 Numbers n such that the bottom entry in the difference table of the divisors of n is 0. 9

%I

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

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

%C Numbers n such that A187202(n) = 0.

%C 11373118351 and 1756410942451 are also in the sequence (not necessarily the next two terms). - _Donovan Johnson_, Aug 05 2011

%C 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

%C No other terms up to 3*10^9. - _Michel Marcus_, Apr 09 2017

%C a(9) > 6*10^10. 138662735650982521 and 168248347462416481 are also terms. - _Giovanni Resta_, Apr 12 2017

%e 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.

%t 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 *)

%o (Haskell)

%o import Data.List (elemIndices)

%o a187204 n = a187204_list !! (n-1)

%o a187204_list = map (+ 1) $ elemIndices 0 $ map a187202 [1..]

%o -- _Reinhard Zumkeller_, Aug 02 2011

%o (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

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

%K nonn,more,hard

%O 1,1

%A _Omar E. Pol_, Aug 01 2011

%E Suggested by _T. D. Noe_ in the "history" of A187203.

%E a(6)-a(7) from _Donovan Johnson_, Aug 03 2011

%E a(8) from _Giovanni Resta_, Apr 11 2017

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Last modified October 17 01:03 EDT 2019. Contains 328103 sequences. (Running on oeis4.)