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 A244394 Consider a number n with m decimal digits, m>1. The sequence lists the numbers n such that the prefix of length m-1 and the suffix of length m-1 both have the same sum of divisors. 1

%I #21 Jul 02 2014 17:10:27

%S 11,22,33,44,55,66,77,88,99,111,222,333,335,444,534,551,555,579,589,

%T 666,682,777,888,954,956,999,1102,1111,2138,2204,2222,2246,2649,3190,

%U 3333,4354,4408,4428,4444,5332,5376,5555,5644,5925,6294,6666,6933,7480,7528

%N Consider a number n with m decimal digits, m>1. The sequence lists the numbers n such that the prefix of length m-1 and the suffix of length m-1 both have the same sum of divisors.

%C Let x(0)x(1)... x(q-1)x(q) denote the decimal expansion of a number n. The sequence lists the numbers n such that sigma(p) = sigma(s) where p is the prefix x(0)x(1)... x(q-1) and s is the suffix x(1)... x(q-1)x(q).

%e 5376 is in the sequence because sigma(537) = sigma(376) = 720.

%p with(numtheory):

%p for n from 10 to 10000 do:

%p x:=convert(n, base, 10):n1:=nops(x):

%p s1:=sum('x[i]*10^(i-1) ', 'i'=1..n1-1):

%p s2:=(n-irem(n,10))/10:

%p x1:=sigma(s1):x2:=sigma(s2):

%p if x1 = x2

%p then

%p printf(`%d, `, n):

%p else

%p fi:

%p od:

%Y Cf. A244282, A244283.

%K nonn,base

%O 1,1

%A _Michel Lagneau_, Jun 27 2014

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Last modified September 9 21:36 EDT 2024. Contains 375765 sequences. (Running on oeis4.)