A353551 - OEIS

A353551

a(n) = Sum_{k=1..n} tau(k^3), where tau is the number of divisors function A000005.

0, 1, 5, 9, 16, 20, 36, 40, 50, 57, 73, 77, 105, 109, 125, 141, 154, 158, 186, 190, 218, 234, 250, 254, 294, 301, 317, 327, 355, 359, 423, 427, 443, 459, 475, 491, 540, 544, 560, 576, 616, 620, 684, 688, 716, 744, 760, 764, 816, 823, 851, 867, 895, 899, 939, 955, 995

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Karl-Heinz Hofmann, Table of n, a(n) for n = 0..10000

FORMULA

a(n) = Sum_{k=1..n} tau(k^3).

a(n) = a(n-1) + A048785(n) for n >= 1, a(0) = 0.

EXAMPLE

A048785(0) = 0

+ A048785(1) = 1

+ A048785(2) = 4

+ A048785(3) = 4

------------------

= A353551(3) = 9

MAPLE

a:= proc(n) option remember; `if`(n=0, 0, a(n-1)+numtheory[tau](n^3)) end:

seq(a(n), n=0..100); # Alois P. Heinz, May 08 2022

MATHEMATICA

Accumulate[Join[{0}, Table[DivisorSigma[0, k^3], {k, 1, 50}]]] (* Amiram Eldar, May 08 2022 *)

PROG

(Python) from sympy import divisor_count

def A048785(n): return divisor_count(n**3)

def A353551(n): return sum(A048785(n) for n in range(1, n))

print([A353551(n) for n in range(1, 58)])

(PARI) a(n) = sum(k=1, n, numdiv(k^3)); \\ Michel Marcus, May 08 2022

(Python)

from math import prod

from sympy import factorint

def A353551(n): return sum(prod(3*e+1 for e in factorint(k).values()) for k in range(1, n+1)) # Chai Wah Wu, May 10 2022

CROSSREFS

Partial sums of A048785.

Cf. A000005, A006218, A061503 (squares).

Sequence in context: A315101 A315102 A315103 * A315104 A315105 A315106

Adjacent sequences: A353548 A353549 A353550 * A353552 A353553 A353554

KEYWORD

nonn

AUTHOR

Karl-Heinz Hofmann, May 07 2022

STATUS

approved