The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
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!)
A369720 The sum of divisors of the smallest cubefull number that is a multiple of n. 5
1, 15, 40, 15, 156, 600, 400, 15, 40, 2340, 1464, 600, 2380, 6000, 6240, 31, 5220, 600, 7240, 2340, 16000, 21960, 12720, 600, 156, 35700, 40, 6000, 25260, 93600, 30784, 63, 58560, 78300, 62400, 600, 52060, 108600, 95200, 2340, 70644, 240000, 81400, 21960, 6240 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
a(n) = A000203(A356193(n)).
Multiplicative with a(p) = p^3 + p^2 + p + 1 for e <= 2, and a(p^e) = (p^(e+1)-1)/(p-1) for e >= 3.
a(n) >= A000203(n), with equality if and only if n is cubefull (A036966).
Dirichlet g.f.: zeta(s-1) * zeta(s) * Product_{p prime} (1 + 1/p^(s-3) + 1/p^(s-2) - 1/p^(2*s-4) - 1/p^(2*s-3) - 1/p^(2*s-2) + 1/p^(4*s-4)).
Sum_{k=1..n} a(k) ~ c * n^4 / 4, where c = zeta(3) * zeta(4) * Product_{p prime} (1 - 1/p^3 - 1/p^4 + 1/p^7 + 1/p^12 - 1/p^13) = 1.00015013207437782094... .
MATHEMATICA
f[p_, e_] := (p^If[e <= 2, 4, e + 1]-1)/(p-1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 50]
PROG
(PARI) a(n) = {my(f = factor(n)); for(i = 1, #f~, if(f[i, 2] <= 2, f[i, 2] = 3)); sigma(f); }
CROSSREFS
Sequence in context: A126950 A091847 A062222 * A369758 A325659 A223432
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Jan 30 2024
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 June 13 17:15 EDT 2024. Contains 373391 sequences. (Running on oeis4.)