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 A345874 #7 Jul 04 2021 16:02:46 %S A345874 1,2,2,3,2,3,2,4,2,4,2,4,2,3,3,5,2,4,2,5,2,3,2,5,2,3,3,4,2,4,2,6,2,4, %T A345874 2,6,2,3,2,6,2,4,2,4,3,3,2,6,2,3,3,4,2,5,2,5,2,3,2,5,2,3,4,7,2,4,2,6, %U A345874 2,3,2,7,2,4,2,4,2,3,2,7,2,4,2,5,3,3,2 %N A345874 a(n) is the number of distinct pairs of positive integers (u, v) such that A065157(u, v) = n. %C A345874 If A065157(u, v) = n then u is a divisor of n. %H A345874 Rémy Sigrist, <a href="/A345874/a345874.gp.txt">PARI program for A345874</a> %H A345874 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a> %H A345874 <a href="/index/Di#divisors">Index entries for sequences related to divisors</a> %F A345874 a(n) <= A000005(n). %F A345874 a(n) >= 2 for any n > 1 (as A065157(1, n) = A065157(n, 1) = n). %F A345874 a(2^k) = k + 1 for any k >= 0. %F A345874 a(2^k - 1) = A000005(k) for any k > 0. %e A345874 For n = 10: %e A345874 - the table A065157(u, v) begins (with terms > 10 replaced by dots): %e A345874 u\v| 1 2 3 4 5 6 7 8 9 10 %e A345874 ---+---------------------------------- %e A345874 1| 1 2 3 4 5 6 7 8 9 10 %e A345874 2| 2 4 10 8 . . . . . . %e A345874 3| 3 6 . . . . . . . . %e A345874 4| 4 8 . . . . . . . . %e A345874 5| 5 10 . . . . . . . . %e A345874 6| 6 . . . . . . . . . %e A345874 7| 7 . . . . . . . . . %e A345874 8| 8 . . . . . . . . . %e A345874 9| 9 . . . . . . . . . %e A345874 10| 10 . . . . . . . . . %e A345874 - the value 10 appears 4 times, %e A345874 - so a(10) = 4. %o A345874 (PARI) See Links section. %Y A345874 Cf. A000005, A065157. %K A345874 nonn,base %O A345874 1,2 %A A345874 _Rémy Sigrist_, Jun 27 2021