login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A360970 Multiplicative with a(p^e) = e^3, p prime and e > 0. 4
1, 1, 1, 8, 1, 1, 1, 27, 8, 1, 1, 8, 1, 1, 1, 64, 1, 8, 1, 8, 1, 1, 1, 27, 8, 1, 27, 8, 1, 1, 1, 125, 1, 1, 1, 64, 1, 1, 1, 27, 1, 1, 1, 8, 8, 1, 1, 64, 8, 8, 1, 8, 1, 27, 1, 27, 1, 1, 1, 8, 1, 1, 8, 216, 1, 1, 1, 8, 1, 1, 1, 216, 1, 1, 8, 8, 1, 1, 1, 64, 64 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
LINKS
FORMULA
Dirichlet g.f.: zeta(s) * Product_{primes p} (1 + (7*p^(2*s) - 2*p^s + 1) / (p^s*(p^s - 1)^3)).
Sum_{k=1..n} a(k) ~ c * n, where c = Product_{primes p} (1 + (7*p^2 - 2*p + 1) / (p*(p-1)^3)) = 109.601930729008995813857898403091253809628920963774227252953...
a(n) = A005361(n)^3.
MAPLE
f:= proc(n) local t;
mul(t^3, t = ifactors(n)[2][.., 2]);
end proc:
map(f, [$1..100]); # Robert Israel, Mar 29 2023
MATHEMATICA
g[p_, e_] := e^3; a[1] = 1; a[n_] := Times @@ g @@@ FactorInteger[n]; Array[a, 100]
PROG
(PARI) for(n=1, 100, print1(direuler(p=2, n, (1 - 3*X + 10*X^2 - 3*X^3 + X^4)/(1-X)^4)[n], ", "))
CROSSREFS
Sequence in context: A066341 A181064 A010153 * A363918 A133421 A128881
KEYWORD
nonn,mult
AUTHOR
Vaclav Kotesovec, Feb 27 2023
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 19 06:44 EDT 2024. Contains 371782 sequences. (Running on oeis4.)