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Search: id:A144262
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| A144262 |
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a(n) = smallest k such that k*n is not a Niven (or Harshad) number. |
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+0
5
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| 11, 7, 5, 4, 3, 11, 2, 2, 11, 13, 1, 8, 1, 1, 1, 1, 1, 161, 1, 8, 5, 1, 1, 4, 1, 1, 7, 1, 1, 13, 1, 1, 1, 1, 1, 83, 1, 1, 1, 4, 1, 4, 1, 1, 11, 1, 1, 2, 1, 5, 1, 1, 1, 537, 1, 1, 1, 1, 1, 83, 1, 1, 3, 1, 1, 1, 1, 1, 1, 5, 1, 68, 1, 1, 1, 1, 1, 1, 1, 2, 7, 1, 1, 2, 1, 1, 1, 1, 1, 211, 1, 1, 1, 1, 1, 1, 1, 1, 1
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Niven (or Harshad) numbers are numbers that can be divided by the sum of their digits.
If n is not a Niven number then a(n) is obviously 1. Some terms are rather large: a(108) = 3611, a(540) = 537037; see also A144375 and A144376.
Does a(n) exist for all n? - Klaus Brockhaus, Sep 19 2008
a(n) should exist for all n since the density of the Niven numbers is zero and it has been proved that arbitrarily large gaps exist between Niven numbers. [From Sergio Pimentel (ferdiego(AT)suddenlink.com), Sep 20 2008]
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LINKS
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Eric Weisstein's World of Mathematics, Harshad Number
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EXAMPLE
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a(2) = 7 since 2, 4, 6, 8, 10 and 12 are all Niven numbers; but 7*2 = 14 is not.
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PROGRAM
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(PARI) digitsum(n) = {local(s=0); while(n, s+=n%10; n\=10); s} {for(n=1, 100, k=1; while((p=k*n)%digitsum(p)==0, k++); print1(k, ", "))} /* Klaus Brockhaus, Sep 19 2008 */
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CROSSREFS
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Cf. A005349 (Niven numbers), A144261 (smallest k such that k*n is a Niven number), A144375 (records in A144262), A144376 (where records occur in A144262).
Sequence in context: A132361 A155914 A087896 this_sequence A110093 A166521 A060954
Adjacent sequences: A144259 A144260 A144261 this_sequence A144263 A144264 A144265
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KEYWORD
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base,nonn
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AUTHOR
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Sergio Pimentel (ferdiego(AT)suddenlink.net), Sep 16 2008
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EXTENSIONS
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Edited by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Sep 19 2008
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