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Search: id:A108825
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| A108825 |
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Numbers n such that n divides the sum of the digits of n!. |
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+0
6
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| 1, 2, 3, 9, 15, 18, 21, 27, 72, 81, 234, 462, 502, 522, 1314, 1323, 3789, 3897, 6462, 10470, 17532, 17820, 28503, 48248, 48254, 48303, 48644, 48856, 223551, 226149, 227406
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Especially for larger values, terms can be expected to occur near values of k such that 4.5 times the number of digits in k!, not counting the digits in the string of trailing zeros, is approximately an integer multiple (m) of k. As m increases, such values of k approach k = e * 100^(m/9 + 1/8) - Jon E. Schoenfield (jonscho(AT)hiwaay.net), Jun 08 2007
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EXAMPLE
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3!=6; (6 mod 3)=0.
9!=362880; 3+6+2+8+8=27; (27 mod 9)=0.
522 is a term because the digit sum of 522!, 4698, is divisible by 522.
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MAPLE
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P:=proc(n) local i, k, w; for i from 1 by 1 to n do w:=0; k:=i!; while k>0 do w:=w+k-(trunc(k/10)*10); k:=trunc(k/10); od; if (w mod i)=0 then print(i); fi; od; end: P(700); - Paolo P. Lava & Giorgio Balzarotti (ppl(AT)spl.at), Jun 04 2007
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MATHEMATICA
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Do[If[Mod[Plus @@ IntegerDigits[n! ], n] == 0, Print[n]], {n, 1, 10000}]
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CROSSREFS
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Cf. A125526, A125724.
Sequence in context: A139816 A083303 A078610 this_sequence A109663 A056702 A091361
Adjacent sequences: A108822 A108823 A108824 this_sequence A108826 A108827 A108828
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KEYWORD
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more,nonn,base
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AUTHOR
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Ryan Propper (rpropper(AT)stanford.edu), Jul 11 2005
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EXTENSIONS
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a(20)-a(28) from Ray Chandler (rayjchandler(AT)sbcglobal.net), Jul 25 2005
Further terms from Jon E. Schoenfield (jonscho(AT)hiwaay.net), Jun 08 2007
Edited by N. J. A. Sloane (njas(AT)research.att.com), Jul 02 2008 at the suggestion of R. J. Mathar
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