A093811 Sum of the digital products of the divisors of n.

1, 3, 4, 7, 6, 12, 8, 15, 13, 8, 2, 18, 4, 14, 14, 21, 8, 29, 10, 12, 13, 8, 7, 34, 16, 18, 27, 34, 19, 22, 4, 27, 14, 22, 28, 53, 22, 36, 34, 20, 5, 33, 13, 28, 43, 33, 29, 72, 44, 18, 16, 32, 16, 63, 32, 72, 48, 61, 46, 28, 7, 18, 40, 51, 39, 62, 43, 74, 64, 34, 8, 83, 22, 52, 59

Offset: 1

Author

Jason Earls, May 20 2004

Keywords

• base
• easy
• nonn

Comments

The first few n such that a(n) = n are: 1,14,27,156,196. Are there any more?

Inverse Moebius transform of A007954(n). a(n) = A007954(n) * A000012(n), where operation * denotes Dirichlet convolution for n >= 1. Dirichlet convolution of functions b(n), c(n) is function a(n) = b(n) * c(n) = Sum_{d|n} b(d)*c(n/d). Simultaneously holds Dirichlet multiplication: a(n) * A008683(n) = A007954(n). [From Jaroslav Krizek, Mar 22 2009]

Examples

			a(1234)=69 because the divisors of 1234 are: [1, 2, 617, 1234] and
1+2+(6*1*7)+(1*2*3*4) = 69.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A007954, A008683.

Programs

Maple

A093811 := proc(n::integer)
    local a,d ;
    a := 0 ;
    for d in numtheory[divisors](n) do
        a := a+A007954(d) ;
    end do:
end proc: # R. J. Mathar, Oct 02 2019

Mathematica

Table[Total[Times@@IntegerDigits[#]&/@Divisors[n]],{n,100}] (* Harvey P. Dale, Jun 02 2022 *)