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A068721
Arithmetic derivative of cubes: a(n) = 3*n^2*A003415(n).
5
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
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
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Feb 26 2002
STATUS
approved