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A331573 The bottom entry in the forward difference table of the Euler totient function phi for 1..n. 1
1, 0, 1, -2, 5, -14, 39, -102, 247, -558, 1197, -2494, 5167, -10850, 23311, -51132, 113333, -250694, 547871, -1175998, 2475153, -5117486, 10439895, -21142030, 42777735, -86960284, 178221401, -368541508, 767762191, -1606535062, 3365499467, -7038925364, 14671422797, -30450115592 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

a(2n) is a nonpositive even number while a(2n-1) is an odd positive number.

Abs(a(n)) < abs(a(n+1)) for 1 < n < 8000.

Indices n <= 8000 such that a(n) is prime: 4, 5, 13, 15, 19, 135, 3095, 3131, 7405.

LINKS

Table of n, a(n) for n=1..34.

EXAMPLE

a(8) = -102 because:

1     1     2     2     4     2     6     4  (first 8 terms of A000010)

   0     1     0     2    -2     4    -2     (first 7 terms of A057000)

      1    -1     2    -4     6     6

        -2     3    -6    10   -12

            5    -9    16   -22

             -14    25   -38

                 39   -63

                  -102

The first principal right descending diagonal is this sequence.

MATHEMATICA

f[n_] := Differences[ Array[ EulerPhi, n], n -1][[1]]; Array[f, 34] (* or *)

nmx = 34; Join[ {1}, Differences[ Array[ EulerPhi, nmx], #][[1]] & /@ Range[nmx - 1]]

CROSSREFS

Cf. A187202, A000010, A057000.

Sequence in context: A148314 A001011 A148315 * A141752 A291729 A142586

Adjacent sequences:  A331570 A331571 A331572 * A331574 A331575 A331576

KEYWORD

sign

AUTHOR

Robert G. Wilson v, Jan 20 2020

STATUS

approved

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Last modified July 14 15:26 EDT 2020. Contains 335729 sequences. (Running on oeis4.)