|
%I #12 Jun 02 2022 20:43:23
%S 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,
%T 34,19,22,4,27,14,22,28,53,22,36,34,20,5,33,13,28,43,33,29,72,44,18,
%U 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
%N Sum of the digital products of the divisors of n.
%C The first few n such that a(n) = n are: 1,14,27,156,196. Are there any more?
%C 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]
%H Harvey P. Dale, <a href="/A093811/b093811.txt">Table of n, a(n) for n = 1..1000</a>
%e a(1234)=69 because the divisors of 1234 are: [1, 2, 617, 1234] and
%e 1+2+(6*1*7)+(1*2*3*4) = 69.
%p A093811 := proc(n::integer)
%p local a,d ;
%p a := 0 ;
%p for d in numtheory[divisors](n) do
%p a := a+A007954(d) ;
%p end do:
%p end proc: # _R. J. Mathar_, Oct 02 2019
%t Table[Total[Times@@IntegerDigits[#]&/@Divisors[n]],{n,100}] (* _Harvey P. Dale_, Jun 02 2022 *)
%Y Cf. A007954, A008683.
%K base,easy,nonn
%O 1,2
%A _Jason Earls_, May 20 2004
|
