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 A143275 A054525 * A029935. 1
 1, 1, 3, 3, 7, 3, 11, 7, 12, 7, 19, 9, 23, 11, 21, 16, 31, 12, 35, 21, 33, 19, 43, 21, 48, 23, 44, 33, 55, 21, 59, 36, 57, 31, 77, 36, 71, 35, 69, 49, 79, 33, 83, 57, 84, 43, 91, 48, 108, 48, 93, 69, 103, 44, 133, 77, 105, 55, 115, 63, 119, 59, 132, 80, 161, 57, 131, 93, 129 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 FORMULA Möbius transform (A054525) of A029935: (1, 2, 4, 5, 8, 8, 12, 12, 16, ...). Multiplicative with a(p) = 2*p - 3 and a(p^e) = (e*(p-1) + p + 2) * (p-1)^2 * p^(e-3) for e > 1. - Amiram Eldar, Aug 31 2023 EXAMPLE a(4) = 3 = (0, -1, 0, 1) dot (1, 2, 4, 5) = (0 - 2 + 0 + 5), where K(0, -1, 0, 1) = row 4 of A054525 and A143275 = (1, 2, 4, 5, 8, 8, 12, ...). MAPLE read("transforms") : A029935 := proc(n) local a, d ; a := 0 ; for d in numtheory[divisors](n) do a := a+ numtheory[phi](d)*numtheory[phi](n/d); od; RETURN(a) ; end: a029935 := [seq(A029935(n), n=1..300)] ; a143275 := MOBIUS(a029935) ; # R. J. Mathar, Jan 19 2009 MATHEMATICA f[p_, e_] := If[e > 1, (e*(p-1) + p + 2) * (p-1)^2 * p^(e-3), 2*p - 3]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Aug 31 2023 *) CROSSREFS Cf. A029935, A054525. Sequence in context: A164928 A253249 A069949 * A083262 A122978 A119347 Adjacent sequences: A143272 A143273 A143274 * A143276 A143277 A143278 KEYWORD nonn,easy,mult AUTHOR Gary W. Adamson, Aug 03 2008 EXTENSIONS More terms from R. J. Mathar, Jan 19 2009 STATUS approved

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Last modified May 21 07:02 EDT 2024. Contains 372729 sequences. (Running on oeis4.)