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A109669
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Numbers n such that the sum of the digits of sigma(n)^phi(n) is divisible by n.
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0
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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
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1,2
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COMMENTS
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No more terms < 58000. - Emeric Deutsch, Jul 25 2006
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LINKS
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Table of n, a(n) for n=1..24.
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EXAMPLE
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The digits of sigma(3735)^phi(3735) sum to 33615 and 33615 is divisible by 3735, so 3735 is in the sequence.
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MAPLE
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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
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MATHEMATICA
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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 *)
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CROSSREFS
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Sequence in context: A126487 A241965 A182193 * A164905 A142106 A078851
Adjacent sequences: A109666 A109667 A109668 * A109670 A109671 A109672
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KEYWORD
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base,more,nonn
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AUTHOR
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Ryan Propper, Aug 06 2005
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EXTENSIONS
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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
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STATUS
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approved
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