A240900 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}{phi(Sum_{j=1..i}{d_(k-j+1)*10^(i-j)})} (see example below).

11, 13, 17, 19, 23, 29, 1363, 2983, 23389, 101299, 132011, 136363, 144133, 198169, 1076441, 1222423, 1973987, 2185367, 2191463, 2673623, 11491523, 18160663, 127666453, 262001569, 264484657, 2080368463, 2763449953, 20603271407, 28272595783

Offset

1,1

Links

Table of n, a(n) for n=1..29.

Example

If n = 132011, starting from the most significant digit, let us cut the number into the set 1, 13, 132, 1320, 13201. We have:
phi(1) = 1;
phi(13) = 12;
phi(132) = 40;
phi(1320) = 320;
phi(13201) = 12852
and 1 + 12 + 40 + 320 + 12852 = 13225 = sigma(132011) - 132011.

Maple

with(numtheory); P:=proc(q) local a, 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;
if sigma(n)-n=a then print(n); fi; od; end: P(10^9);

Crossrefs

Cf. A000010, A000203, A240894-A240899, A240901, A240902.

Sequence in context: A038842 A293660 A046117 * A091923 A046501 A050719

Adjacent sequences: A240897 A240898 A240899 * A240901 A240902 A240903

Keyword

nonn,base,more

Author

Paolo P. Lava, Apr 14 2014

Extensions

a(15)-a(29) from Giovanni Resta, Apr 15 2014

Status

approved