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A248904 Consider a decimal number of k>=2 digits z = d_(k)*10^(k-1) + d_(k-1)*10^(k-2) + … + d_(2)*10 + d_(1) and the sum y = Sum_{x=2..k} {Sum_{j=1..k-x}{d_(j+x-1)*10^(j-1)} - Sum_{j=1..x-1}{d_(j)*10^(j-1)}}. Sequence lists the numbers for which y = tau(z), where tau(z) is the number of divisors of z . 0

%I

%S 31,51,53,62,95,97,209,318,429,443,553,886,887,2165,2217,4387,4439,

%T 5498,5553,6714,7775,8932,10548,56105,56107,78292,78320,78324,78328,

%U 88887,89439,99998,110747,111083,221861,332969,438885,667023,667025,671853,888880,1107504

%N Consider a decimal number of k>=2 digits z = d_(k)*10^(k-1) + d_(k-1)*10^(k-2) + … + d_(2)*10 + d_(1) and the sum y = Sum_{x=2..k} {Sum_{j=1..k-x}{d_(j+x-1)*10^(j-1)} - Sum_{j=1..x-1}{d_(j)*10^(j-1)}}. Sequence lists the numbers for which y = tau(z), where tau(z) is the number of divisors of z .

%e For 78324 the sum y is: (7832 - 4) + (783 - 24) + (78 - 324) + (7 - 8324) = 7828 + 759 - 246 - 8317 = 24 and tau(78324) = 24.

%p with(numtheory): P:=proc(q) local a,k,n;

%p for n from 1 to q do a:=0;

%p for k from 1 to ilog10(n) do a:=a+trunc(n/10^k)-(n mod 10^k); od;

%p if a=tau(n) then print(n); fi; od; end: P(10^9);

%Y CF. A000005.

%K nonn,base

%O 1,1

%A _Paolo P. Lava_, Mar 06 2015

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Last modified August 10 14:50 EDT 2020. Contains 336381 sequences. (Running on oeis4.)