A244068 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 Sum_{i=1..k-1}{sigma(Sum_{j=1..i}{d_(j)*10^(j-1)})} = Sum_{i=1..k-1}{phi(Sum_{j=1..i}{d_(k-j+1)*10^(i-j)})} (see example below).

11, 12, 35, 38, 57, 59, 152, 599, 2812, 3419, 3915, 6733, 11671, 16706, 16714, 16858, 25303, 26752, 128257, 171762, 238571, 265872, 345715, 375923, 486141, 496975, 573433, 1492832, 2324671, 2944061

Offset

1,1

Links

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

Example

If n = 345715, starting from the least significant digit, let us cut the number into the set {5, 15, 715, 5715, 45715}. We have:
phi(5) = 4;
phi(15) = 8;
phi(715) = 480;
phi(5715) = 3024;
phi(45715) = 35520.
Then, starting from the most significant digit, let us cut the number into the set {3, 34, 345, 3457, 34571}. We have:
sigma(3) = 4;
sigma(34) = 54;
sigma(345) = 576;
sigma(3457) = 3458;
sigma(34571) = 34944.
Finally, 4 + 8 + 480 + 3024 + 35520 = 4 + 54 + 576 + 3458 + 34944 = 39036.

Maple

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

Crossrefs

Cf. A000010, A000203, A240894-A240903, A241207, A241502, A241503, A244069.

Sequence in context: A309631 A075559 A080138 * A041252 A041250 A225299

Adjacent sequences: A244065 A244066 A244067 * A244069 A244070 A244071

Keyword

nonn,base

Author

Paolo P. Lava, Jun 19 2014

Status

approved