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
Keywords
Examples
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
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
-
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] -
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);}