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Search: id:A109669
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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
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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No more terms < 58000. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 25 2006
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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 (deutsch(AT)duke.poly.edu), 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}]
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CROSSREFS
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Sequence in context: A070302 A125329 A126487 this_sequence A142106 A078851 A142649
Adjacent sequences: A109666 A109667 A109668 this_sequence 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 (rpropper(AT)stanford.edu), Aug 06 2005
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 25 2006
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