A027435 -id:A027435 - cp's OEIS frontend

A014666 Erroneous version of A027435.

1, 2, 4, 6, 10, 11, 17, 21, 27, 29, 39, 42, 54, 58, 63, 71, 87, 90, 108, 114, 121, 126

Offset: 1

dead

Former title: Partial sums of A014665. - Sean A. Irvine, Nov 15 2018

S. W. Golomb, personal communication, Svalbard, Norway, 7/97.

For n>1: # of positive integers u <= n(n-1) such that p^H_p(u)<=n for all p<=u, where H_p(u) = highest power of p dividing u.

A014665 Number of new fractions m/n < 1, where (m,n)=1 and "new" means the value of m*n has not occurred before.

Original entry on oeis.org

1, 1, 2, 2, 4, 1, 6, 4, 6, 2, 10, 3, 12, 3, 5, 8, 16, 3, 18, 6, 7, 5, 22, 5, 20, 6, 18, 8, 28, 4, 30, 16, 12, 8, 18, 9, 36, 9, 14, 12, 40, 6, 42, 13, 17, 11, 46, 11, 42, 10, 19, 15, 52, 9, 25, 20, 21, 14, 58, 10, 60, 15, 28, 32, 29, 9, 66, 21, 26, 11, 70, 20, 72, 18, 23, 23, 42, 11, 78, 23, 54

Offset: 1

N. J. A. Sloane

nonn

			{1}, {1/2}, {1/3,2/3}, {1/4,3/4}, {1/5,...,4/5}, {5/6}, ...

S. W. Golomb, personal communication, Svalbard, Norway, 7/97.

Andrew Howroyd, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe).

Cf. A027435, A236309.

a[1] = 1;
a[n_] := Sum[Boole[GCD[i, n] == 1 && Sum[t = i*n/d; Boole[GCD[t, d] == 1 && t < d < n], {d, Divisors[i*n]}] == 0], {i, 1, n - 1}];
Array[a, 100] (* Jean-François Alcover, Sep 05 2019, from PARI *)

a(n)=if(n==1, 1, sum(i=1, n-1, gcd(i,n) == 1 && 0==sumdiv(i*n, d, my(t=i*n/d); gcd(t,d)==1 && dAndrew Howroyd, Nov 16 2018

Example corrected by and more terms from Olivier Gérard, Feb 1999

cp's OEIS Frontend

A014666 Erroneous version of A027435.

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A014665 Number of new fractions m/n < 1, where (m,n)=1 and "new" means the value of m*n has not occurred before.

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