A109669 Numbers n such that the sum of the digits of sigma(n)^phi(n) is divisible by n.

1, 19, 126, 162, 231, 255, 717, 1611, 1897, 3231, 3735, 8692, 8774, 10676, 16903, 17299, 22194, 30845, 92049, 309546, 459780, 502302, 763755, 788379

Offset

1,2

Comments

No more terms < 58000. - Emeric Deutsch, Jul 25 2006

Links

Table of n, a(n) for n=1..24.

Example

The digits of sigma(3735)^phi(3735) sum to 33615 and 33615 is divisible by 3735, so 3735 is in the sequence.

Maple

with(numtheory): sd:=proc(n) local nn: nn:=convert(n, base, 10): add(nn[j], j=1..nops(nn)) end: a:=proc(n) if sd(sigma(n)^phi(n)) mod n = 0 then n else fi end: seq(a(n), n=1..2000); # Emeric Deutsch, Jul 25 2006

Mathematica

Do[s = DivisorSigma[1, n]^EulerPhi[n]; k = Plus @@ IntegerDigits[s]; If[Mod[k, n] == 0, Print[n]], {n, 1, 10^4}]
Select[Range[100000], Divisible[Total[IntegerDigits[DivisorSigma[1, #]^ EulerPhi[ #]]], #]&] (* Harvey P. Dale, Jan 03 2012 *)

Crossrefs

Sequence in context: A126487 A241965 A182193 * A164905 A142106 A078851

Adjacent sequences: A109666 A109667 A109668 * A109670 A109671 A109672

Keyword

base,more,nonn

Author

Ryan Propper, Aug 06 2005

Extensions

More terms from Emeric Deutsch, Jul 25 2006

One more term (a(19)) from Harvey P. Dale, Jan 03 2012

a(20)-a(24) from Lars Blomberg, Dec 02 2016

Status

approved