A068721 Arithmetic derivative of cubes: a(n) = 3*n^2*A003415(n).

0, 12, 27, 192, 75, 540, 147, 2304, 1458, 2100, 363, 6912, 507, 5292, 5400, 24576, 867, 20412, 1083, 28800, 13230, 18876, 1587, 76032, 18750, 30420, 59049, 75264, 2523, 83700, 2883, 245760, 45738, 65892, 44100

Offset

1,2

Links

Bruno Berselli, Table of n, a(n) for n = 1..1000

Formula

a(n) = A003415(A000578(n)).

Prog

(Magma) Ad:=func<h | h*(&+[Factorisation(h)[i][2]/Factorisation(h)[i][1]: i in [1..#Factorisation(h)]])>; [0] cat [Ad(n^3): n in [2..40]]; // Bruno Berselli, Oct 22 2013
(Python)
from sympy import factorint
def A068721(n): return 3*n**2*sum((n*e//p for p, e in factorint(n).items())) if n > 1 else 0 # Chai Wah Wu, Nov 03 2022

Crossrefs

Cf. A068720, A000578, A003415.

Sequence in context: A151542 A069550 A079705 * A228181 A196208 A196475

Adjacent sequences: A068718 A068719 A068720 * A068722 A068723 A068724

Keyword

nonn

Author

Reinhard Zumkeller, Feb 26 2002

Status

approved