A269669 Numbers whose Euler totient function is equal to the sum of some fixed power of their digits.

1, 2, 20, 40, 228, 352, 712, 813, 835, 2079, 4020, 28248, 46460, 62460, 498708, 622802, 2440224, 8430382, 31119492, 620412393, 640668240, 9142803052, 11922717895, 12712197589, 15559421974, 19179475160

Offset

1,2

Comments

a(27) > 4*10^11. - Giovanni Resta, Apr 08 2016

Links

Table of n, a(n) for n=1..26.

Paolo P. Lava, Terms of the sequence and their fixed power

Example

2^3 + 0^3 = 8 and phi(20) = 8;
2^4 + 8^4 + 2^4 + 4^4 + 8^4 = 8480 and phi(28248) = 8480.

Maple

with(numtheory); P:= proc(q) local a, b, c, d, k, n, ok; print(1); for n from 2 to q do d:=phi(n); a:=[]; b:=n; ok:=0;
for k from 1 to ilog10(n)+1 do if (b mod 10)>1 then ok:=1; fi; a:=[(b mod 10), op(a)]; b:=trunc(b/10); od; b:=-1; c:=0;
if ok=1 then while c<d do b:=b+1;
if b>0 then c:=add(a[k]^b, k=1..nops(a)); else for k from 1 to nops(a) do if a[k]=0 then c:=0; break; else c:=c+1; fi; od; fi; od; if c=d then print(n); fi; fi; od; end: P(10^9);

Mathematica

Select[Range[10^6], Function[k, AnyTrue[Total[IntegerDigits[k]^#] & /@ Range@ 6, # == EulerPhi@ k &]]] (* Michael De Vlieger, Mar 03 2016, Version 10 *)

Crossrefs

Cf. A000010.

Sequence in context: A050684 A073214 A293356 * A293930 A357485 A194999

Adjacent sequences: A269666 A269667 A269668 * A269670 A269671 A269672

Keyword

nonn,easy,base

Author

Paolo P. Lava, Mar 03 2016

Extensions

a(20)-a(26) from Giovanni Resta, Apr 08 2016

Status

approved