cp's OEIS Frontend

A248955 Number of polynomials a_k*x^k + ... + a_1*x + n with k > 0, integer coefficients and distinct positive integer roots and positive integers n.

%I A248955 #22 Mar 24 2017 00:47:57
%S A248955 1,3,3,5,3,9,3,9,5,9,3,17,3,9,9,13,3,17,3,17,9,9,3,31,5,9,9,17,3,29,3,
%T A248955 19,9,9,9,35,3,9,9,31,3,29,3,17,17,9,3,49,5,17,9,17,3,31,9,31,9,9,3,
%U A248955 61,3,9,17,27,9,29,3,17,9,29,3,67,3,9,17,17,9
%N A248955 Number of polynomials a_k*x^k + ... + a_1*x + n with k > 0, integer coefficients and distinct positive integer roots and positive integers n.
%C A248955 If D_n is the set of all positive divisors of n, then a(n) gives the number of all subsets of D_n for which the product of all their elements is a divisor of n. a(n) depends only on the prime signature of n.
%H A248955 Reiner Moewald, <a href="/A248955/b248955.txt">Table of n, a(n) for n = 1..2159</a>
%F A248955 a(p) = 3, for p prime. - _Michel Marcus_, Nov 07 2014
%e A248955 a(2) = 3: -2x+2; -x+2; x^2 - 3x + 2.
%o A248955 (PARI) padbin(n, len) = {b = binary(n); while(length(b) < len, b = concat(0, b);); b;}
%o A248955 a(n) = {d = divisors(n); nbd = #d; nbts = 2^nbd-1; nbs = 0; for (i=1, nbts, bin = padbin(i, nbd); prd = prod(j=1, nbd,  if (bin[j], d[j], 1)); if (n % prd == 0, nbs++);); nbs;} \\ _Michel Marcus_, Nov 07 2014
%Y A248955 Cf. A248410, A248956.
%K A248955 nonn
%O A248955 1,2
%A A248955 _Reiner Moewald_, Oct 17 2014