

A240896


Consider a number of k digits n = d_(k)*10^(k1) + d_(k1)*10^(k2) + … + d_(2)*10 + d_(1). Sequence lists the numbers n such that sigma(n)  n = Sum_{i=1..k1}{phi(Sum_{j=1..i}{d_(j)*10^(j1)})}} (see example below).


2




OFFSET

1,1


COMMENTS

a(9) > 10^10.  Giovanni Resta, Apr 16 2014


LINKS

Table of n, a(n) for n=1..8.


EXAMPLE

If n = 4351, starting from the least significant digit, let us cut the number into the set 1, 51, 351. We have:
phi(1) = 1;
phi(51) = 32;
phi(351) = 216
and 1 + 32 + 216 = 249 = sigma(4351)  4351.


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+phi(n mod 10^k); k:=k+1; od;
if sigma(n)n=a then print(n); fi; od; end: P(10^9);


CROSSREFS

Cf. A000010, A000203, A240894, A240895, A240897A240902.
Sequence in context: A181182 A089347 A287312 * A040985 A061599 A153128
Adjacent sequences: A240893 A240894 A240895 * A240897 A240898 A240899


KEYWORD

nonn,more,base


AUTHOR

Paolo P. Lava, Apr 14 2014


EXTENSIONS

a(7)a(8) from Giovanni Resta, Apr 16 2014


STATUS

approved



