A240901 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_(k-j+1)*10^(i-j)})} (see example below)

16566, 767869500, 8187453840

Offset

1,1

Comments

a(4) > 3*10^10. - Giovanni Resta, Apr 15 2014

Links

Table of n, a(n) for n=1..3.

Example

If n = 16566, starting from the most significant digit, let us cut the number into the set 1, 16, 165, 1656. We have:
sigma(1) = 1;
sigma(16) = 31;
sigma(165) = 288;
sigma(1656) = 4680
and 1 + 31 + 288 + 4680 = 5000 = phi(16566).

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

Crossrefs

Cf. A000010, A000203, A240894-A240900, A240902.

Sequence in context: A091089 A109028 A193244 * A234894 A283028 A344241

Adjacent sequences: A240898 A240899 A240900 * A240902 A240903 A240904

Keyword

nonn,base,more

Author

Paolo P. Lava, Apr 14 2014

Extensions

a(2)-a(3) from Giovanni Resta, Apr 15 2014

Status

approved