A241207 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)})} - Sum_{i=1..k-1}{sigma(Sum_{j=1..i}{d_(k-j+1)*10^(i-j)})} (see example below)

23, 47, 142, 161, 433, 1435, 1900, 6679, 48917, 197943, 257941, 3916321, 48635983, 1142976889, 1811878288

Offset

1,1

Comments

a(16) > 10^10. - Giovanni Resta, May 23 2016

Links

Table of n, a(n) for n=1..15.

Example

If n = 48917, starting from the least significant digit, let us cut the number into the set 7, 17, 917, 8917. We have:
sigma(7) = 8;
sigma(17) = 18;
sigma(917) = 1056;
sigma(8917) = 9196.
Then, starting from the most significant digit, let us cut the number into the set 4, 48, 489, 4891. We have:
sigma(4) = 7;
sigma(48) = 124;
sigma(489) = 656;
sigma(4891) = 5032.
Finally,
8 + 18 + 1056 + 9196 - (7 + 124 + 656 + 5032) = 4459 = sigma(48917) - 48917.

Maple

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

Crossrefs

Cf. A000203, A240894-A240903.

Sequence in context: A042048 A347008 A239563 * A042050 A139857 A139900

Adjacent sequences: A241204 A241205 A241206 * A241208 A241209 A241210

Keyword

nonn,base,more

Author

Paolo P. Lava, Apr 17 2014

Extensions

a(1)-a(2) corrected and a(12)-a(15) added by Giovanni Resta, May 23 2016

Status

approved