A082849 Product of cototient values of consecutive integers.

0, 1, 2, 2, 4, 4, 4, 12, 18, 6, 8, 8, 8, 56, 56, 8, 12, 12, 12, 108, 108, 12, 16, 80, 70, 126, 144, 16, 22, 22, 16, 208, 234, 198, 264, 24, 20, 300, 360, 24, 30, 30, 24, 504, 504, 24, 32, 224, 210, 570, 532, 28, 36, 540, 480, 672, 630, 30, 44, 44, 32, 864, 864, 544, 782

Offset

1,3

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Laurenţiu Panaitopol, Asymptotical formula for a(n) = n - e(n), Bull. Math. Soc. Sci. Math. Roumanie, Vol. 42 (90), No. 3 (1999), pp. 271-277.

Formula

a(n) = A051953(n) * A051953(n+1).

Sum_{k=1..n} a(k) ~ c * n^3 + O(n^2 * log(n)^2), where c = (1/3) * (1 + Product_{p prime} (1 - 2/p^2)) - 4/Pi^2 = 0.03559329841.... (Panaitopol, 1999). - Amiram Eldar, Mar 09 2021

Mathematica

f[x_] := x-EulerPhi[x] tpr=Table[f[w+1]*f[w], {w, 1, 128}]
Times@@@Partition[Table[n-EulerPhi[n], {n, 70}], 2, 1] (* Harvey P. Dale, Nov 17 2020 *)

Prog

(PARI) p=2; forprime(q=3, 97, print1((p-eulerphi(p))*(q-eulerphi(q))", "); p=q) \\ Charles R Greathouse IV, Nov 16 2012

Crossrefs

Cf. A051953, A065474, A083538-A083555.

Sequence in context: A083549 A083548 A376944 * A211882 A284432 A284435

Adjacent sequences: A082846 A082847 A082848 * A082850 A082851 A082852

Keyword

nonn

Author

Labos Elemer, May 22 2003

Status

approved