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 A140706 A054525 * A014683; a(n) = Sum_{d|n} mu(d)*A014683(n/d). 1
 1, 2, 3, 1, 5, 0, 7, 4, 5, 2, 11, 5, 13, 4, 6, 8, 17, 7, 19, 9, 10, 8, 23, 8, 19, 10, 18, 13, 29, 11, 31, 16, 18, 14, 22, 12, 37, 16, 22, 16, 41, 15, 43, 21, 25, 20, 47, 16, 41, 21, 30, 25, 53, 18, 38, 24, 34, 26, 59, 15, 61, 28, 37, 32, 46, 23, 67, 33, 42, 27, 71, 24, 73, 34, 41 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) = n iff n is prime. LINKS Antti Karttunen, Table of n, a(n) for n = 1..10000 FORMULA Möbius transform of A014683: (1, 3, 4, 4, 6, 6, 8, 8, 9, 10, ...); where A014683(n) = n if n is not prime; but (n+1) if n is prime. a(n) = Sum_{d|n} A008683(d)*A014683(n/d), where A008683 is Moebius mu function. - Antti Karttunen, Jul 28 2017 EXAMPLE a(4) = 1 = (0, -1, 0, 1) dot (1, 3, 4, 4), where (0, -1, 0, 1) = row 4 of triangle A054525. MAPLE read("transforms") : A014683 := proc(n) if isprime(n) then 1+n; else n; fi; end: a014683 := [seq(A014683(n), n=1..150)] ; a140706 := MOBIUS(a014683) ; for i from 1 to nops(a140706) do printf("%d, ", op(i, a140706)) ; od: # R. J. Mathar, Jan 19 2009 MATHEMATICA Table[Sum[MoebiusMu[d] (# + Boole@ PrimeQ@ #) &[n/d], {d, Divisors@ n}], {n, 75}] (* Michael De Vlieger, Jul 29 2017 *) PROG (PARI) A014683(n) = (n+isprime(n)); A140706(n) = sumdiv(n, d, moebius(d)*A014683(n/d)); \\ Antti Karttunen, Jul 28 2017 (Python) from sympy import isprime, mobius, divisors def a014683(n): return n + isprime(n) def a140706(n): return sum([mobius(d)*a014683(n/d) for d in divisors(n)]) print map(a140706, xrange(1, 101)) # Indranil Ghosh, Jul 29 2017 CROSSREFS Cf. A008683, A014683, A054525. Sequence in context: A201737 A080063 A187680 * A200068 A139764 A227643 Adjacent sequences:  A140703 A140704 A140705 * A140707 A140708 A140709 KEYWORD nonn AUTHOR Gary W. Adamson, May 24 2008 EXTENSIONS More terms from R. J. Mathar, Jan 19 2009 Second part added to the name by Antti Karttunen, Jul 28 2017 STATUS approved

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Last modified August 17 11:51 EDT 2019. Contains 326057 sequences. (Running on oeis4.)