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

1,2

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]

Links

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

Example

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

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 *)

Crossrefs

Cf. A007954, A008683.

Sequence in context: A107749 A353783 A367466 * A088000 A284344 A168338

Adjacent sequences: A093808 A093809 A093810 * A093812 A093813 A093814

Keyword

base,easy,nonn

Author

Jason Earls, May 20 2004

Status

approved