A063919 Sum of proper unitary divisors (or unitary aliquot parts) of n, including 1.

1, 1, 1, 1, 1, 6, 1, 1, 1, 8, 1, 8, 1, 10, 9, 1, 1, 12, 1, 10, 11, 14, 1, 12, 1, 16, 1, 12, 1, 42, 1, 1, 15, 20, 13, 14, 1, 22, 17, 14, 1, 54, 1, 16, 15, 26, 1, 20, 1, 28, 21, 18, 1, 30, 17, 16, 23, 32, 1, 60, 1, 34, 17, 1, 19, 78, 1, 22, 27, 74, 1, 18, 1, 40, 29, 24, 19, 90, 1, 22, 1, 44

Offset

1,6

Comments

For definition of unitary divisor see A034448.

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537 (first 1000 terms from Harry J. Smith)

Formula

a(n) = A034460(n), n>1. - R. J. Mathar, Oct 02 2008

For n > 1: a(n) = sum (A077610(n,k): k = 1 .. A034444(n) - 1). - Reinhard Zumkeller, Mar 12 2012

Example

a(10) = 8 because the unitary divisors of 10 are 1, 2, 5 and 10, with sum 18 and 18-10 = 8.

Maple

A063919 := proc(n)
    if n = 1 then
        1;
    else
        A034448(n)-n ;
    end if;
end proc: # R. J. Mathar, May 14 2013

Mathematica

a[n_] := Total[Select[Divisors[n], GCD[#, n/#] == 1&]]-n; a[1] = 1; Table[a[n], {n, 82}] (* Jean-François Alcover, Aug 31 2011 *)

Prog

(PARI) usigma(n) = sumdiv(n, d, if(gcd(d, n/d)==1, d))
{ for (n=1, 1000, if (n>1, a=usigma(n) - n, a=1); write("b063919.txt", n, " ", a) ) } \\ Harry J. Smith, Sep 02 2009
(PARI)
A034460(n) = (sumdivmult(n, d, if(gcd(d, n/d)==1, d))-n); \\ From A034460
A063919(n) = if(1==n, n, A034460(n)); \\ Antti Karttunen, Jun 12 2018
(Haskell)
a063919 1 = 1
a063919 n = sum $ init $ a077610_row n
-- Reinhard Zumkeller, Mar 12 2012

Crossrefs

The values of sequence are A034448(n)-n (for n > 1).

Cf. A001065, A034448, A034460.

Sequence in context: A364944 A320832 A034460 * A308135 A072815 A348979

Adjacent sequences: A063916 A063917 A063918 * A063920 A063921 A063922

Keyword

easy,nonn,nice

Author

Felice Russo, Aug 31 2001

Status

approved