OFFSET
1,2
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Henry Bottomley, Some Smarandache-type multiplicative sequences
FORMULA
From Amiram Eldar, Oct 27 2022: (Start)
Multiplicative with a(p^e) = 1 if e is divisible by 4, and a(p^e) = p^4 otherwise.
Sum_{k=1..n} a(k) ~ c * n^5, where c = (zeta(20)/(5*zeta(4))) * Product_{p prime} (1 - 1/p^2 + 1/p^4 - 1/p^7 + 1/p^8) = 0.123026157003... . (End)
EXAMPLE
a(64) = 16 because smallest 4th power divisible by 64 is 256 and largest 4th power which divides 64 is 16 and 256/16 = 16.
MATHEMATICA
f[p_, e_] := p^If[Divisible[e, 4], 0, 1]; a[n_] := (Times @@ (f @@@ FactorInteger[ n]))^4; Array[a, 100] (* Amiram Eldar, Aug 29 2019*)
PROG
(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i, 2]%4, f[i, 1], 1))^4; } \\ Amiram Eldar, Oct 27 2022
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Henry Bottomley, Jun 25 2000
STATUS
approved