A371599 Numbers of least prime signature (A025487) whose prime factorization has equal number of even and odd exponents.

1, 12, 48, 72, 192, 288, 432, 768, 1152, 1260, 1728, 2592, 3072, 4608, 5040, 6912, 10368, 12288, 12600, 15552, 18432, 20160, 27648, 41472, 45360, 49152, 50400, 62208, 73728, 75600, 80640, 93312, 110592, 165888, 181440, 196608, 201600, 248832, 264600, 294912, 302400

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  A162641(a(n)) = A162642(a(n))
  --  -------  ------------  -----------------------------
   1        1            {}                              0
   2       12         {2,1}                              1
   3       48         {4,1}                              1
   4       72         {3,2}                              1
   5      192         {6,1}                              1
   6      288         {5,2}                              1
   7      432         {4,3}                              1
   8      768         {8,1}                              1
   9     1152         {7,2}                              1
  10     1260     {2,2,1,1}                              2
  11     1728	    {6,3}                              1
  12     2592         {5,4}                              1

Mathematica

fun[p_, e_] := (-1)^e; q[n_] := Module[{f = FactorInteger[n]}, n == 1 || (f[[-1, 1]] == Prime[Length[f]] && Max@ Differences[f[[;; , 2]]] < 1 && Plus @@ fun @@@ f == 0)]; Select[Range[3*10^5], q]

Prog

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

Crossrefs

Intersection of A025487 and A187039.

Cf. A162641, A162642, A371600.

Sequence in context: A324747 A044114 A323008 * A044495 A213493 A009958

Adjacent sequences: A371596 A371597 A371598 * A371600 A371601 A371602

Keyword

nonn

Author

Amiram Eldar, Mar 29 2024

Status

approved