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2, 0, 0, 4, 0, 7, 0, 8, 9, 11, 0, 12, 0, 15, 16, 16, 0, 18, 0, 20, 22, 23, 0, 24, 25, 27, 27, 28, 0, 29, 0, 32, 34, 35, 36, 36, 0, 39, 40, 40, 0, 41, 0, 44, 45, 47, 0, 48, 49, 50, 52, 52, 0, 54, 56, 56, 58, 59, 0, 60, 0, 63, 63, 64, 66, 65, 0, 68, 70, 69, 0, 72, 0, 75, 75, 76, 78, 77, 0, 80, 81, 83, 0, 84, 86, 87, 88, 88, 0
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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For n>1, a(n) = n iff mu(n) = 0; 0 if n is prime; and (n+1) iff mu(n) = 1.
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LINKS
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FORMULA
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a(n) = n + A140664(n), where A140664 = (1, -2, -3, 0, -5, 1, -7, 0, 0, 1,...)
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EXAMPLE
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MATHEMATICA
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Table[Exp[MangoldtLambda[n]]*MoebiusMu[n] + n, {n, 100}] (* G. C. Greubel, Feb 13 2019 *)
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PROG
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(PARI)
(Sage)
def A140668(n): return simplify(exp(add(moebius(d)*log(n/d) for d in divisors(n))))*moebius(n) + n
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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