A240895 Consider a number of k digits n = d_(k)*10^(k-1) + d_(k-1)*10^(k-2) + … + d_(2)*10 + d_(1). Sequence lists the numbers n such that sigma(n) - n = Sum_{i=1..k-1}{sigma(Sum_{j=1..i}{d_(j)*10^(j-1)})} (see example below).

11, 25, 31, 41, 61, 71, 341, 671, 2119, 10231, 39579, 52231, 60341, 402959, 1288689, 1393059, 1956759, 16752951, 108659999, 181704519, 794033191, 1062726071, 3518397571, 4062296851, 4085227151, 7015608139

Offset

1,1

Comments

a(27) > 10^10. - Giovanni Resta, Apr 16 2014

Links

Table of n, a(n) for n=1..26.

Example

If n = 52231, starting from the least significant digit, let us cut the number into the set 1, 31, 231, 2231. We have:
sigma(1) = 1;
sigma(31) = 32;
sigma(231) = 384;
sigma(2231) = 2352
and 1 + 32 + 384 + 2352 = 2769 = sigma(52231) - 52231.

Maple

with(numtheory); P:=proc(q) local a, k, n;
for n from 2 to q do a:=0; k:=1; while (n mod 10^k)<n do
a:=a+sigma(n mod 10^k); k:=k+1; od;
if sigma(n)-n=a then print(n); fi; od; end: P(10^9);

Crossrefs

Cf. A000203, A240894, A240896-A240902.

Sequence in context: A251412 A286279 A125868 * A301635 A031025 A140675

Adjacent sequences: A240892 A240893 A240894 * A240896 A240897 A240898

Keyword

nonn,more,base

Author

Paolo P. Lava, Apr 14 2014

Extensions

a(14), a(18)-a(26) from Giovanni Resta, Apr 16 2014

Status

approved