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 A144262 a(n) = smallest k such that k*n is not a Niven (or Harshad) number. 5
 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; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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, Sep 20 2008] LINKS Eric Weisstein's World of Mathematics, Harshad Number EXAMPLE a(2) = 7 since 2, 4, 6, 8, 10 and 12 are all Niven numbers; but 7*2 = 14 is not. PROG (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 */ CROSSREFS 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 * A110093 A187563 A089487 Adjacent sequences:  A144259 A144260 A144261 * A144263 A144264 A144265 KEYWORD base,nonn AUTHOR Sergio Pimentel, Sep 16 2008 EXTENSIONS Edited by Klaus Brockhaus, Sep 19 2008 STATUS approved

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