A185373 The numerator of the fraction |n^2/A049417(n)-A064380(n)|.

1, 1, 1, 1, 0, 1, 4, 1, 5, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 7, 5, 1, 2, 1, 2, 9, 3, 1, 1, 1, 4, 11, 11, 25, 2, 1, 1, 9, 2, 1, 11, 1, 4, 3, 7, 1, 2, 1, 2, 1, 13, 1, 3, 1, 13, 49, 17, 1, 0, 1, 1, 49, 16, 25, 1, 1, 17, 19, 35, 1, 14, 1, 2

Offset: 2

Author

Vladimir Shevelev, Feb 17 2011

Keywords

• nonn
• frac
• less

Comments

n^2/A049417(n) is a multiplicative function, whereas A064380 is not. This sequence here measures the (small) differences n^2/A049417(n)-A064380(n) = 1/3, 1/4, 1/5, 1/6, 0, 1/8, 4/15, 1/10, 5/9, 1/12, 1/5 ...

Links

• Amiram Eldar, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A064380, A049417, A185383 (denominators)

Programs

Mathematica

f[p_, e_] := p^(2^(-1 + Position[Reverse @ IntegerDigits[e, 2], ?(# == 1 &)])); isigma[1] = 1; isigma[n] := Times @@ (Flatten@(f @@@ FactorInteger[n]) + 1);
infCoprimeQ[n1_, n2_] := Module[{g = GCD[n1, n2]}, If[g == 1, True, AllTrue[ FactorInteger[g][[;; , 1]], BitAnd @@ IntegerExponent[{n1, n2}, #] == 0 &]]];
a[n_] := Abs[Numerator[n^2 / isigma[n] - Sum[Boole[infCoprimeQ[j, n]], {j, 1, n-1}]]]; Array[a, 100, 2] (* Amiram Eldar, Mar 20 2025 *)