cp's OEIS Frontend

A280163 Least number k such that sopfr(k) - sopf(k) = k/n, -1 if such a number does not exist.

%I A280163 #14 Jan 03 2017 12:07:53
%S A280163 4,9,32,25,12,49,48,54,20,121,96,169,28,45,144,289,162,361,160,63,44,
%T A280163 529,-1,250,52,-1,224,841,60,961,320,99,68,175,180,1369,76,117,240,
%U A280163 1681,84,1849,352,270,92,2209,-1,686,-1,153,416,2809,-1,275,336,171,116
%N A280163 Least number k such that sopfr(k) - sopf(k) = k/n, -1 if such a number does not exist.
%C A280163 a(n) = n^2 for n prime.
%C A280163 Values equal to -1 are hypothetical (tested up to 2*10^10 by _Giovanni Resta_).
%e A280163 a(6) = 12 because 12 is the least number such that sopfr(12) - sopf(12) = 7 - 5 = 2 = 12/6.
%p A280163 with(numtheory): P:=proc(q) local a, j, k, n;
%p A280163 for n from 2 to q do for j from n by n to q do
%p A280163 a:=ifactors(j)[2]; if add(a[k][1]*a[k][2],k=1..nops(a))-add(a[k][1],k=1..nops(a))=j/n then
%p A280163 lprint(n,j); break; fi; od; od; end: P(10^6);
%t A280163 Table[SelectFirst[Range[n^3], Function[k, Total@ # - Total@ Union@ # == k/n &@ Flatten@ Map[ConstantArray[#1, #2] & @@ # &, #] &@ FactorInteger@ k]] /. k_ /; MissingQ@ k -> -1, {n, 2, 58}] (* Version 10.2, or *)
%t A280163 Table[k = 1; While[And[Total@ # - Total@ Union@ # != k/n, k <= n^3] &@ Flatten@ Map[ConstantArray[#1, #2] & @@ # &, #] &@ FactorInteger@ k, k++]; If[k > n^3, -1, k], {n, 2, 58}] (* _Michael De Vlieger_, Dec 28 2016 *)
%Y A280163 Cf. A007947, A008472.
%K A280163 sign
%O A280163 2,1
%A A280163 _Paolo P. Lava_, Dec 27 2016