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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
OFFSET
1,2
COMMENTS
No more terms < 58000. - Emeric Deutsch, Jul 25 2006
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
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