This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A348415 #13 Oct 20 2021 07:16:08 %S A348415 12,88,180,266,321,604,4277,4364,8632,15861,18720,28461,47613,63546, %T A348415 97412,98907,135078,137333,154132,179621,185776,192699,203709,265489, %U A348415 284883,344217,383466,517610,604197,876469,1089604,1277518,1713865,1839123,1893268,2349390 %N A348415 Numbers k such that k and k+1 have the same denominator of the harmonic means of their divisors. %C A348415 Numbers k such that A099378(k) = A099378(k+1). %C A348415 The common denominators of k and k+1 are 7, 45, 91, 30, 36, 133, 96, 637, ... %C A348415 Can 3 consecutive numbers have the same denominator of harmonic mean of divisors? There are no such numbers below 10^10. %H A348415 Amiram Eldar, <a href="/A348415/b348415.txt">Table of n, a(n) for n = 1..300</a> %e A348415 12 is a term since the harmonic means of the divisors of 12 and 13 are 18/7 and 13/7, respectively, and both have the denominator 7. %t A348415 dh[n_] := Denominator[DivisorSigma[0, n]/DivisorSigma[-1, n]]; Select[Range[10^6], dh[#] == dh[# + 1] &] %o A348415 (PARI) f(n) = my(d=divisors(n)); denominator(#d/sum(k=1, #d, 1/d[k])); \\ A099378 %o A348415 isok(k) = f(k) == f(k+1); \\ _Michel Marcus_, Oct 20 2021 %Y A348415 Cf. A099377, A099378. %Y A348415 Similar sequences: A002961, A238380. %K A348415 nonn %O A348415 1,1 %A A348415 _Amiram Eldar_, Oct 17 2021