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A093811 Sum of the digital products of the divisors of n. 3
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
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
Sequence in context: A107749 A353783 A367466 * A088000 A284344 A168338
KEYWORD
base,easy,nonn
AUTHOR
Jason Earls, May 20 2004
STATUS
approved

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Last modified March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)