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A082849
Product of cototient values of consecutive integers.
1
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
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
KEYWORD
nonn
AUTHOR
Labos Elemer, May 22 2003
STATUS
approved