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 A349222 #10 Nov 12 2021 04:35:51 %S A349222 5,14,44,55,152,1334,1634,1652,2204,2232,2295,2685,3195,4256,7191, %T A349222 8216,9144,9503,9844,10152,18423,19491,20118,27404,30247,33998,38180, %U A349222 42818,45716,48364,51624,79316,79338,84134,117116,122073,124676,125811,139460,157640,166624 %N A349222 Numbers k such that k and k+1 have the same average of unitary divisors. %C A349222 The average of the unitary divisors of k is equal to A034448(k)/A034444(k). %C A349222 Terms k such that k and k+1 are squarefree are also terms of A238380. The terms that are not in A238380 are 44, 55, 152, 1652, 2204, 2232, 2295, 3195, 4256, ... %C A349222 The average is an integer for the first 1000 terms. Are there terms with a noninteger average? %H A349222 Amiram Eldar, <a href="/A349222/b349222.txt">Table of n, a(n) for n = 1..1000</a> %e A349222 5 is a term since the average of the unitary divisors of 5 is (1 + 5)/2 = 3, and the average of the unitary divisors of 6 is (1 + 2 + 3 + 6)/4 = 3. %e A349222 44 is a term since the average of the unitary divisors of 44 is (1 + 4 + 11 + 44)/4 = 15, and the average of the unitary divisors of 45 is (1 + 5 + 9 + 45)/4 = 15. %t A349222 m[1] = 1; m[n_] := (Times @@ (1 + Power @@@ (f = FactorInteger[n])))/2^Length[f]; Select[Range[10^5], m[#] == m[# + 1] &] %Y A349222 Cf. A007674, A034444, A034448, A103826, A238380. %K A349222 nonn %O A349222 1,1 %A A349222 _Amiram Eldar_, Nov 11 2021