A112622 If p^b(p,n) is the highest power of the prime p dividing n, then a(n) = product_{p|n} b(p,n)^b(p,n).
1, 1, 1, 4, 1, 1, 1, 27, 4, 1, 1, 4, 1, 1, 1, 256, 1, 4, 1, 4, 1, 1, 1, 27, 4, 1, 27, 4, 1, 1, 1, 3125, 1, 1, 1, 16, 1, 1, 1, 27, 1, 1, 1, 4, 4, 1, 1, 256, 4, 4, 1, 4, 1, 27, 1, 27, 1, 1, 1, 4, 1, 1, 4, 46656, 1, 1, 1, 4, 1, 1, 1, 108, 1, 1, 4, 4, 1, 1, 1, 256, 256, 1, 1, 4, 1, 1, 1, 27, 1, 4, 1, 4, 1, 1, 1, 3125, 1, 4, 4, 16, 1, 1, 1, 27, 1
Offset: 1
Examples
45 = 3^2 * 5^1. So a(45) = 2^2 * 1^1 = 4. 72 = 2^3 * 3^2. So a(72) = 3^3 * 2^2 = 108.
Links
- Antti Karttunen, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
f[n_] := Block[{fi = Last@Transpose@FactorInteger@n}, Times @@ (fi^fi)]; Rest@Array[f, 93] (* Robert G. Wilson v *) -
PARI
a(n)=local(v,r,i);v=factorint(n);r=1;for(i=1,matsize(v)[1],r*=v[i,2]^v[i,2]);r (Herrgesell)
Extensions
More terms from Robert G. Wilson v and Lambert Herrgesell (zero815(AT)googlemail.com), Dec 27 2005
Corrected the starting offset, data section extended to 105 terms - Antti Karttunen, May 28 2017
Comments