

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
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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_{dn} 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



