

A109669


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


0



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



