login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A333753 Sum of prime power divisors of n that are <= sqrt(n). 3
0, 0, 0, 2, 0, 2, 0, 2, 3, 2, 0, 5, 0, 2, 3, 6, 0, 5, 0, 6, 3, 2, 0, 9, 5, 2, 3, 6, 0, 10, 0, 6, 3, 2, 5, 9, 0, 2, 3, 11, 0, 5, 0, 6, 8, 2, 0, 9, 7, 7, 3, 6, 0, 5, 5, 13, 3, 2, 0, 14, 0, 2, 10, 14, 5, 5, 0, 6, 3, 14, 0, 17, 0, 2, 8, 6, 7, 5, 0, 19, 12, 2, 0, 16, 5, 2, 3, 14, 0, 19 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Table of n, a(n) for n=1..90.

FORMULA

G.f.: Sum_{p prime, k>=1} p^k * x^(p^(2*k)) / (1 - x^(p^k)).

MATHEMATICA

Table[DivisorSum[n, # &, # <= Sqrt[n] && PrimePowerQ[#] &], {n, 1, 90}]

nmax = 90; CoefficientList[Series[Sum[Boole[PrimePowerQ[k]] k x^(k^2)/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

PROG

(PARI) a(n) = sumdiv(n, d, if ((d^2<=n) && isprimepower(d), d)); \\ Michel Marcus, Apr 03 2020

CROSSREFS

Cf. A023889, A066839, A069289, A069293, A097974, A246655, A333750, A333751, A333752.

Sequence in context: A278922 A163169 A097974 * A139036 A292129 A291970

Adjacent sequences:  A333750 A333751 A333752 * A333754 A333755 A333756

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Apr 03 2020

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 25 19:39 EST 2021. Contains 341618 sequences. (Running on oeis4.)