A085073 Smallest k such that n+k and n*k have the same prime signature, or 0 if no such number exists.

2, 1, 7, 41, 15, 134, 3, 127, 11, 2, 3, 548, 2, 1, 3, 389, 5, 582, 2, 316, 1, 38, 3, 2216, 3, 2, 13, 212, 5, 2742, 2, 1669, 1, 1, 31, 2764, 2, 1, 13, 1094, 4, 2298, 3, 1, 123, 14, 11, 8912, 3, 202, 17, 2, 2, 1146, 23, 904, 1, 26, 3, 11028, 13, 22, 57, 3581, 37, 1194, 2, 172, 15

Offset

1,1

Links

Michel Marcus, Table of n, a(n) for n = 1..3000

Example

a(6) = 379 as 6*379 = 2*3*379 and 6+379 = 385 = 5*7*11 both have prime signature p*q*r.

Maple

s:= proc(n) s(n):= sort(map(i-> i[2], ifactors(n)[2])) end:
a:= proc(n) option remember; local k; for k
       while s(n*k)<>s(n+k) do od; k
    end:
seq(a(n), n=1..70);  # Alois P. Heinz, Mar 06 2019

Mathematica

kmax = 10^6;
s[n_] := FactorInteger[n][[All, 2]] // Sort;
a[n_] := Module[{k}, If[n == 1, Return[2]]; For[k = 1, k <= kmax, k++, If[s[n k] == s[n+k], Return[k]]]; 0];
Array[a, 70] (* Jean-François Alcover, Nov 17 2020 *)

Prog

(PARI) sgntr(n) = vecsort(factor(n)[, 2]~);
a(n) = {my(k=1); while (sgntr(n+k) != sgntr(n*k), k++); k; } \\ Michel Marcus, Nov 17 2020

Crossrefs

Cf. A052213 (a(n)=1), A085072.

Sequence in context: A320519 A183272 A138346 * A131288 A111789 A179447

Adjacent sequences: A085070 A085071 A085072 * A085074 A085075 A085076

Keyword

nonn

Author

Amarnath Murthy, Jul 01 2003

Extensions

Corrected by Jason Earls, Jul 10 2003

More terms from David Wasserman, Jan 12 2005

Status

approved