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A269669 Numbers whose Euler totient function is equal to the sum of some fixed power of their digits. 1
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 (list; graph; refs; listen; history; text; internal format)
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 A194999 A280436

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

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Last modified September 25 09:40 EDT 2021. Contains 347654 sequences. (Running on oeis4.)