A240897 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 phi(n) = Sum_{i=1..k-1}{sigma(Sum_{j=1..i}{d_(j)*10^(j-1)})} (see example below).

26, 36, 370, 570, 3270, 11746, 21630, 24490, 24806, 56980, 117404, 468430, 595270, 1228070, 3390486, 4784660, 7898490, 9773610, 10529610, 10993626, 12835226, 13094276, 27797386, 30987000, 64644060, 216393030, 291661606, 660619830, 990261270, 1217516566

Offset

1,1

Links

Table of n, a(n) for n=1..30.

Example

If n = 11746, starting from the least significant digit, let us cut the number into the set 6, 46, 746, 1746. We have:
sigma(6) = 12;
sigma(46) = 72;
sigma(746) = 1122;
sigma(1746) = 3822
and 12 + 72 + 1122 + 3822 = 5028 = phi(11746).

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 phi(n)=a then print(n); fi; od; end: P(10^9);

Crossrefs

Cf. A000010, A000203, A240894-A240896, A240898-A240902.

Sequence in context: A103079 A046468 A138065 * A034096 A034106 A239604

Adjacent sequences: A240894 A240895 A240896 * A240898 A240899 A240900

Keyword

nonn,base

Author

Paolo P. Lava, Apr 14 2014

Extensions

a(14)-a(30) from Giovanni Resta, Apr 16 2014

Status

approved