A371600 - OEIS

%I #8 Mar 30 2024 05:33:52

%S 1,60,2160,12600,18480,77760,180180,216000,453600,665280,2646000,

%T 2799360,3880800,7776000,10810800,16329600,16336320,23950080,32016600,

%U 45360000,66528000,95256000,100776960,139708800,214414200,232792560,279936000,389188800,555660000,587865600

%N Numbers of least prime signature (A025487) whose prime factorization has equal sum of even and odd exponents.

%H Amiram Eldar, <a href="/A371600/b371600.txt">Table of n, a(n) for n = 1..10000</a>

%e The prime signatures of the first 12 terms are:

%e    n     a(n)     signature  A350386(a(n)) = A350387(a(n))

%e   --  -------  ------------  -------------   -------------

%e    1        1            {}             0                0

%e    2       60       {1,1,2}             2            1+1=2

%e    3     2160       {1,3,4}             4            1+3=4

%e    4    12600     {1,2,2,3}         2+2=4            1+3=4

%e    5    18480   {1,1,1,1,4}             4        1+1+1+1=4

%e    6    77760       {1,5,6}             6            1+5=6

%e    7   180180 {1,1,1,1,2,2}         2+2=4        1+1+1+1=4

%e    8   216000       {3,3,6}             6            3+3=6

%e    9   453600     {1,2,4,5}         2+4=6            1+5=6

%e   10   665280   {1,1,1,3,6}             6        1+1+1+3=6

%e   11  2646000     {2,3,3,4}         2+4=6            3+3=6

%e   12  2799360       {1,7,8}             8            1+7=8

%t fun[p_, e_] := (-1)^e * e; q[n_] := Module[{f = FactorInteger[n]}, n == 1 || (f[[-1, 1]] == Prime[Length[f]] && Plus @@ fun @@@ f == 0 && Max@ Differences[f[[;; , 2]]] < 1)]; Select[Range[4*10^6], q]

%o (PARI) is(n) = {my(f = factor(n), p = f[, 1], e = f[, 2]); n == 1 || (sum(i = 1, #e, (-1)^e[i] * e[i]) == 0 && e == vecsort(e, , 4) && primepi(p[#p]) == #p);}

%Y Intersection of A025487 and A356413.

%Y Cf. A350386, A350387, A371599.

%K nonn

%O 1,2

%A _Amiram Eldar_, Mar 29 2024