A200723 Bi-unitary Euler function of n.

1, 1, 3, 6, 10, 10, 21, 28, 36, 32, 55, 53, 78, 66, 69, 120, 136, 112, 171, 144, 153, 170, 253, 211, 300, 240, 351, 300, 406, 237, 465, 496, 384, 416, 445, 539, 666, 522, 558, 633, 820, 444, 903, 780, 772, 770, 1081, 887, 1176, 912, 951, 1104

Offset

1,3

Comments

a(n) is the sum over all entries equal to 1 in row A165430(n.,), weighted by the column index.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Laszlo Toth, On the bi-unitary analogues of Euler's arithmetical function and the gcd-sum function J. Int. Seq. 12 (2009) # 09.5.2.

Formula

a(6) = 1*1 + 4*1 +5*1 = 10 corresponding to the three 1's in row 6 of A165430.

Maple

A200723 := proc(n)
        local a, k ;
        a := 0 ;
        for k from 1 to n do
                if A165430(k, n) = 1 then
                        a := a+ k ;
                end if;
        end do;
        a ;
end proc:
seq(A200723(n), n=1..80) ;

Prog

(Haskell)
a200723 = sum . zipWith (*) [1..] . map a063524 . a165430_row
-- Reinhard Zumkeller, Mar 04 2013
(PARI) udivs(n) = {my(d = divisors(n)); select(x->(gcd(x, n/x)==1), d); }
a(n) = sum(k=1, n, if (vecmax(setintersect(udivs(n), udivs(k))) == 1, k)); \\ Michel Marcus, Jun 28 2023

Crossrefs

Cf. A188999

Sequence in context: A032570 A130483 A115012 * A135738 A307574 A169911

Adjacent sequences: A200720 A200721 A200722 * A200724 A200725 A200726

Keyword

nonn,easy

Author

R. J. Mathar, Nov 21 2011

Status

approved