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 A379723 #22 Jan 04 2025 02:48:43 %S A379723 1,5,10,21,26,50,85,91,122,130,170,210,250,260,290,341,362,455,500, %T A379723 530,546,610,651,820,842,850,962,1050,1220,1300,1365,1370,1450,1682, %U A379723 1700,1810,1850,1911,2210,2366,2451,2500,2562,2650,2810,2900,3172,3255,3410,3482 %N A379723 Possible values of the sum of squares of divisors function (A001157). %C A379723 The distinct values of the sigma_2(n) function, in ascending order. %C A379723 The asymptotic density of this sequence is 0 (Niven, 1951). %C A379723 5460 = sigma_2(60) and 5461 = sigma_2(64) are two consecutive integers in this sequence. Are there any other such pairs? There are none below 10^10. %H A379723 Amiram Eldar, <a href="/A379723/b379723.txt">Table of n, a(n) for n = 1..10000</a> %H A379723 Max Alekseyev, <a href="https://oeis.org/wiki/User:Max_Alekseyev/gpscripts#Inversion_of_Multiplicative_Functions">PARI/GP Scripts for Miscellaneous Math Problems: Inversion of Multiplicative Functions</a> (invphi.gp). %H A379723 Ivan Niven, <a href="https://doi.org/10.1090/S0002-9904-1951-09543-9">The asymptotic density of sequences</a>, Bull. Amer. Math. Soc., Vol. 57 (1951), pp. 420-434. See Theorem 3, p. 429. %t A379723 seq[lim_] := Select[Union[DivisorSigma[2, Range[lim]]], # <= lim &]; seq[3500] %o A379723 (PARI) is(n) = invsigmaNum(n, 2) > 0; \\ _Amiram Eldar_, Jan 03 2025, using _Max Alekseyev_'s invphi.gp %Y A379723 Cf. A001157, A002191, A002202. %Y A379723 A066872 is a subsequence. %Y A379723 Subsequence of A211347. %K A379723 nonn,easy %O A379723 1,2 %A A379723 _Amiram Eldar_, Jan 03 2025