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 .

31, 51, 53, 62, 95, 97, 209, 318, 429, 443, 553, 886, 887, 2165, 2217, 4387, 4439, 5498, 5553, 6714, 7775, 8932, 10548, 56105, 56107, 78292, 78320, 78324, 78328, 88887, 89439, 99998, 110747, 111083, 221861, 332969, 438885, 667023, 667025, 671853, 888880, 1107504

Offset

1,1

Links

Table of n, a(n) for n=1..42.

Example

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

Maple

with(numtheory): P:=proc(q) local a, k, n;
for n from 1 to q do a:=0;
for k from 1 to ilog10(n) do a:=a+trunc(n/10^k)-(n mod 10^k); od;
if a=tau(n) then print(n); fi; od; end: P(10^9);

Crossrefs

CF. A000005.

Sequence in context: A004224 A194129 A288291 * A068779 A068473 A275628

Adjacent sequences: A248901 A248902 A248903 * A248905 A248906 A248907

Keyword

nonn,base

Author

Paolo P. Lava, Mar 06 2015

Status

approved