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 A243018 Numbers k such that Sum_{i=1..k} phi(i) is divisible by Sum_{i=1..k} d(i), where phi(i) is the Euler totient function of i (A000010), and d(i) is the number of divisors of i (A000005). 0
 1, 5, 19, 21, 154, 604 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(7) > 10^8. - Michel Marcus, Nov 01 2014 a(7), if it exists, is > 10^9. - Vaclav Kotesovec, Oct 16 2018 LINKS FORMULA Numbers k such that A006218(k) divides A002088(k). EXAMPLE phi(1) + phi(2) + phi(3) + phi(4) + phi(5) = 1 + 1 + 2 + 2 + 4 = 10; d(1) + d(2) + d(3) + d(4) + d(5) = 1 + 2 + 2 + 3 + 2 = 10; Finally 10 / 10 = 1. MAPLE with(numtheory):P:=proc(q) local a, b, n; a:=0; b:=0; for n from 1 to q do a:=a+tau(n); b:=b+phi(n); if type(b/a, integer) then print(n); fi; od; end: P(10^10); PROG (PARI) lista(nn) = {se = 0; sn = 0; for (n=1, nn, se += eulerphi(n); sn += numdiv(n); if (se % sn == 0, print1(n, ", ")); ); } \\ Michel Marcus, Nov 01 2014 (Magma) [n:n in [1..1000]| IsIntegral(&+[EulerPhi(m):m in [1..n]]/&+[NumberOfDivisors(m):m in [1..n]])] ; // Marius A. Burtea, Mar 25 2019 CROSSREFS Cf. A000005, A000010, A002088, A006218, A226647. Sequence in context: A212153 A337401 A338127 * A032731 A275954 A087840 Adjacent sequences: A243015 A243016 A243017 * A243019 A243020 A243021 KEYWORD nonn,more AUTHOR Paolo P. Lava, May 29 2014 STATUS approved

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Last modified December 3 23:46 EST 2022. Contains 358544 sequences. (Running on oeis4.)