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A068721
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Arithmetic derivative of cubes: a(n) = 3*n^2*A003415(n).
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5
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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
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OFFSET
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1,2
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LINKS
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FORMULA
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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