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A066959
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Bigomega(n^n) where bigomega(x) is the number of prime factors in x (counted with multiplicity).
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14
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0, 2, 3, 8, 5, 12, 7, 24, 18, 20, 11, 36, 13, 28, 30, 64, 17, 54, 19, 60, 42, 44, 23, 96, 50, 52, 81, 84, 29, 90, 31, 160, 66, 68, 70, 144, 37, 76, 78, 160, 41, 126, 43, 132, 135, 92, 47, 240, 98, 150, 102, 156, 53, 216, 110, 224, 114, 116, 59, 240, 61, 124, 189, 384
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OFFSET
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1,2
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COMMENTS
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Also, a variant of the arithmetic derivative A003415, with f(p)=p (instead of f(p)=1), i.e., f(Product_i p_i^e_i) = Sum_i e_i * Product_i p_i^e_i. - M. F. Hasler, Jul 13 2015
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LINKS
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FORMULA
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Defined by a(p) = p for p prime and a(mn) = a(m)*n + m*a(n). An analogous sequence with a(p) = 1 is A003415. - David W. Wilson, Mar 02 2011
G.f.: x*f'(x), where f(x) = Sum_{p prime, k>=1} x^(p^k)/(1 - x^(p^k)). - Ilya Gutkovskiy, Apr 10 2017
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MATHEMATICA
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PROG
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(PARI) for (n=1, 1000, write("b066959.txt", n, " ", bigomega(n^n)) ) \\ Harry J. Smith, Apr 11 2010
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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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