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Numbers k such that lcm(1,2,3,...,k)/7 equals the denominator of the k-th harmonic number H(k).
12

%I #15 Jan 31 2021 02:38:16

%S 44,45,46,47,48,301,302,303,304,305,306,307,308,309,310,311,312,313,

%T 314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,

%U 331,332,333,334,335,2209,2210,2211,2212,2213,2214,2215,2216,2217,2218,2219

%N Numbers k such that lcm(1,2,3,...,k)/7 equals the denominator of the k-th harmonic number H(k).

%C When 7 occurs in A110566.

%H Amiram Eldar, <a href="/A112815/b112815.txt">Table of n, a(n) for n = 1..10000</a>

%t f[n_] := LCM @@ Range[n]/Denominator[ HarmonicNumber[n]]; Select[ Range[2219], f[ # ] == 7 &]

%o (PARI) isok(n) = lcm(vector(n, i, i)) == 7*denominator(sum(i=1, n, 1/i)); \\ _Michel Marcus_, Mar 07 2018

%Y Cf. A002805, A003418, A110566.

%Y Cf. A098464, A112813, A112814, A112816, A112817, A112818, A112819, A112820, A112821, A112822.

%K nonn

%O 1,1

%A _Robert G. Wilson v_, Sep 17 2005