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 A229501 Numbers k such that Sum_{i=1..k} i' == 0 (mod k), where i' is the arithmetic derivative of i. 2
 1, 6, 344, 1475, 3816, 5463, 18468, 78894, 515108, 566932, 1600370, 14380856, 27129564, 28669993, 31401775, 39638108, 2245196680, 2878016306, 5890364987, 7838325300, 23168759538, 63226475740, 121869542099 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Next term > 10^7. - M. F. Hasler, Sep 25 2013 a(21) > 10^10. - Donovan Johnson, Sep 25 2013 a(24) > 10^12. - Giovanni Resta, Mar 13 2014 LINKS Table of n, a(n) for n=1..23. FORMULA A229501 = { n | A190121(n) = 0 (mod n) }. - M. F. Hasler, Sep 25 2013 EXAMPLE 1' + 2' + 3' + 4' + 5' + 6' = 0 + 1 + 1 + 4 + 1 + 5 = 12, and 12 mod 6 = 0. MAPLE with(numtheory); P:= proc(q) local a, n, p; a:=0; for n from 1 to q do a:=a+n*add(op(2, p)/op(1, p), p=ifactors(n)[2]); if a mod n=0 then print(n); fi; od; end: P(10^6); PROG (PARI) s=0; for(n=1, 1e7, (s+=A003415(n))%n||print1(n", ")) \\ - M. F. Hasler, Sep 25 2013 CROSSREFS Cf. A003415, A227848. Sequence in context: A144849 A212490 A047941 * A289738 A211089 A221923 Adjacent sequences: A229498 A229499 A229500 * A229502 A229503 A229504 KEYWORD nonn,more AUTHOR Paolo P. Lava, Sep 25 2013 EXTENSIONS Double-checked below 10^6 and extended up to 10^7 by M. F. Hasler, Sep 25 2013 a(12)-a(20) from Donovan Johnson, Sep 25 2013 a(21)-a(23) from Giovanni Resta, Mar 13 2014 STATUS approved

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Last modified September 7 11:06 EDT 2024. Contains 375730 sequences. (Running on oeis4.)