A371600 Numbers of least prime signature (A025487) whose prime factorization has equal sum of even and odd exponents.

1, 60, 2160, 12600, 18480, 77760, 180180, 216000, 453600, 665280, 2646000, 2799360, 3880800, 7776000, 10810800, 16329600, 16336320, 23950080, 32016600, 45360000, 66528000, 95256000, 100776960, 139708800, 214414200, 232792560, 279936000, 389188800, 555660000, 587865600

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

The prime signatures of the first 12 terms are:
   n     a(n)     signature  A350386(a(n)) = A350387(a(n))
  --  -------  ------------  -------------   -------------
   1        1            {}             0                0
   2       60       {1,1,2}             2            1+1=2
   3     2160       {1,3,4}             4            1+3=4
   4    12600     {1,2,2,3}         2+2=4            1+3=4
   5    18480   {1,1,1,1,4}             4        1+1+1+1=4
   6    77760       {1,5,6}             6            1+5=6
   7   180180 {1,1,1,1,2,2}         2+2=4        1+1+1+1=4
   8   216000       {3,3,6}             6            3+3=6
   9   453600     {1,2,4,5}         2+4=6            1+5=6
  10   665280   {1,1,1,3,6}             6        1+1+1+3=6
  11  2646000     {2,3,3,4}         2+4=6            3+3=6
  12  2799360       {1,7,8}             8            1+7=8

Mathematica

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]

Prog

(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); }

Crossrefs

Intersection of A025487 and A356413.

Cf. A350386, A350387, A371599.

Sequence in context: A004353 A269284 A004364 * A054623 A075908 A130647

Adjacent sequences: A371597 A371598 A371599 * A371601 A371602 A371603

Keyword

nonn

Author

Amiram Eldar, Mar 29 2024

Status

approved