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A093811 Sum of the digital products of the divisors of n. 2
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..75.

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

CROSSREFS

Cf. A007954, A008683.

Sequence in context: A254981 A116607 A107749 * A088000 A284344 A168338

Adjacent sequences:  A093808 A093809 A093810 * A093812 A093813 A093814

KEYWORD

base,easy,nonn

AUTHOR

Jason Earls, May 20 2004

STATUS

approved

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Last modified June 23 10:51 EDT 2021. Contains 345397 sequences. (Running on oeis4.)