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 A227008 Numbers k such that Sum_{j=1..k} (sigma(j) + phi(j) + tau(j)) == 0 (mod k). 0
 1, 399, 872, 1214, 2090, 5200, 5588, 21208, 29152, 638049, 1627676, 151732410, 274845607, 3224070252, 54892040166, 69020111756, 175288968221 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(17) > 10^11. - Donovan Johnson, Jul 07 2013 a(18) > 5*10^11. - Giovanni Resta, Jul 11 2013 LINKS Table of n, a(n) for n=1..17. EXAMPLE Sum_{j=1..399} sigma(j) = 130973; Sum_{j=1..399} phi(j) = 48518; Sum_{j=1..399} tau(j) = 2453; (130973 + 48518 + 2453) / 399 = 456. MAPLE with(numtheory); ListA227008:=proc(q, h) local a, n; a:=0; for n from 1 to q do a:=a+sigma(n)+phi(n)+tau(n); if (a mod n)=0 then print(n); fi; od; end: ListA227008(10^9); PROG (PARI) s=0; for(n=1, 274845607, s=s+sigma(n)+eulerphi(n)+numdiv(n); if(s%n==0, print(n " " s))) /* Donovan Johnson, Jul 06 2013 */ CROSSREFS Cf. A000005, A000010, A000203. Cf. A006218, A002088, A024916. Cf. A233541. Sequence in context: A202158 A126231 A158317 * A253597 A006972 A216925 Adjacent sequences: A227005 A227006 A227007 * A227009 A227010 A227011 KEYWORD nonn,more AUTHOR Paolo P. Lava, Jun 27 2013 EXTENSIONS a(11)-a(14) from Donovan Johnson, Jul 06 2013 a(15)-a(16) from Donovan Johnson, Jul 07 2013 a(17) from Giovanni Resta, Jul 11 2013 STATUS approved

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Last modified June 23 05:53 EDT 2024. Contains 373629 sequences. (Running on oeis4.)