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 A331813 #14 Feb 10 2020 06:42:56 %S A331813 2,2,2,2,4,4,2,7,2,4,8,2,3,2,2,4,2,64,3,64,4,8,7,4,15,3,50,2,2,50,2,7, %T A331813 29184,2,16,64,4,16,4,385,15,9,313600,2,4,2793,4199,2,4,57600 %N A331813 a(n) is the least k > 1 such that k*A019278(n) belongs to A019278 too, or a(n) = 0 if no such k exists. %C A331813 For the 132 terms (< 5*10^11) of the b-file for A019278, and using an extended list of terms, it can be checked that a(n) is not 0, even if the precise value is not known. For instance, a(51) <= 8097830664651. %C A331813 Then a(52) to a(82) are: 4, 9, 1197, 8, 256, 4, 65155475, 64, 4096, 16, 195205791, 1387, 7, 37791, 4, 119, 8, 35136, 225, 64, 69127695, 2129920, 256, 4, 19671223, 9, 2, 1379763, 8, 90, 4096. And a(83) <= 7758260899200. %C A331813 a(51) and a(83) are > 10^9. %e A331813 With A019278 starting as 1, 2, 4, 8, 15, 16, 21, 24, 42, 60, 64, ... %e A331813 one gets the proper multiples 2, 4, 8, 16, 60, 64, ... %e A331813 and so the sequence begins: 2, 2, 2, 2, 4, 4, ... %o A331813 (PARI) a(n, v019278) = my(m = v019278[n]); my(k=2, y = k*m); while (denominator(sigma(sigma(y))/y) != 1, k++; y += m); k; %Y A331813 Cf. A019278 (integers m such that sigma(sigma(m))/m is an integer). %K A331813 nonn,more %O A331813 1,1 %A A331813 _Michel Marcus_, Jan 27 2020