A143615 Triangle A054521 * A000005 as a vector.

1, 1, 3, 3, 8, 3, 14, 7, 14, 8, 27, 7, 35, 12, 20, 18, 50, 11, 58, 16, 35, 24, 74, 15, 68, 29, 54, 29, 101, 15, 111, 39, 64, 41, 84, 26, 140, 47, 78, 40, 158, 24, 168, 51, 75, 61, 186, 34, 170, 49, 111, 66, 217, 39, 160, 65, 131, 80, 247, 32, 261, 84, 122, 92, 197, 45, 292, 92, 162, 60, 312, 55, 326, 104, 135, 106, 263, 55, 356, 85, 206

Offset

1,3

Links

Table of n, a(n) for n=1..81.

Formula

Triangle A054521 * A000005 as a vector; where 1's indicate the relative primes of n by rows and A000005 = d(n): (1, 2, 2, 3, 2, 4, 2, 4, 3,...)

a(n) = Sum_{ m=1..n and gcd(n,m)=1 } tau(m), where tau(m)=A000005(m). A211932(n)+a(n) = A006218(n). - Naohiro Nomoto, Aug 05 2012

Example

a(8) = 7 since the relative primes of 8 are (1, 3, 5, 7). a(8) = d(1) + d(3) + d(5) + d(7) = 1 + 2 + 2 + 2. Or, a(8) = 7 = (1, 0, 1, 0, 1, 0, 1, 0) dot (1, 2, 2, 3, 2, 4, 2, 4), where (1, 0, 1, 0, 1, 0, 1, 0) = row 8 of triangle A054521 and d(n) = (1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 2,...).
a(7) = 14 = (1, 1, 1, 1, 1, 1, 0) dot (1, 2, 2, 3, 2, 4, 2) = (d(1) + d(2) + d(3) + d(4) + d(5) + d(6)).

Maple

A143615 := proc(n)
    local a, m;
    a := 0 ;
    for m from 1 to n do
        if gcd(m, n) = 1 then
        a := a+numtheory[tau](m) ;
        end if;
    end do:
    a ;
end proc: # R. J. Mathar, Aug 08 2012

Crossrefs

Cf. A054521, A000005, A143614.

Sequence in context: A212809 A294643 A029614 * A199337 A279789 A249389

Adjacent sequences: A143612 A143613 A143614 * A143616 A143617 A143618

Keyword

nonn

Author

Gary W. Adamson, Aug 27 2008

Extensions

More terms from Naohiro Nomoto, Aug 05 2012

Status

approved