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 A342768 #18 Sep 13 2021 09:19:53
%S A342768 1,2,3,8,5,12,7,32,27,20,11,48,13,28,45,128,17,108,19,80,63,44,23,192,
%T A342768 125,52,243,112,29,180,31,512,99,68,175,432,37,76,117,320,41,252,43,
%U A342768 176,405,92,47,768,343,500,153,208,53,972,275,448,171,116,59,720
%N A342768 a(n) = A342767(n, n).
%C A342768 This sequence has similarities with A087019.
%C A342768 These are the positions of first appearances of each positive integer in A346701, and also in A346703. - _Gus Wiseman_, Aug 09 2021
%H A342768 Rémy Sigrist, <a href="/A342768/b342768.txt">Table of n, a(n) for n = 1..10000</a>
%H A342768 Rémy Sigrist, <a href="/A342768/a342768.gp.txt">PARI program for A342768</a>
%H A342768 <a href="/index/Di#dismal">Index entries for sequences related to dismal (or lunar) arithmetic</a>
%F A342768 a(n) = n iff n = 1 or n is a prime number.
%F A342768 a(p^k) = p^(2*k-1) for any k > 0 and any prime number p.
%F A342768 A007947(a(n)) = A007947(n).
%F A342768 A001222(a(n)) = 2*A001222(n) - 1 for any n > 1.
%F A342768 From _Gus Wiseman_, Aug 09 2021: (Start)
%F A342768 A001221(a(n)) = A001221(n).
%F A342768 If g = A006530(n) is the greatest prime factor of n, then a(n) = n^2/g.
%F A342768 a(n) = A129597(n)/2.
%F A342768 (End)
%e A342768 For n = 42:
%e A342768 - 42 = 2 * 3 * 7, so:
%e A342768 2 3 7
%e A342768 x 2 3 7
%e A342768 -------
%e A342768 2 3 7
%e A342768 2 3 3
%e A342768 + 2 2 2
%e A342768 -----------
%e A342768 2 2 3 3 7
%e A342768 - hence a(42) = 2 * 2 * 3 * 3 * 7 = 252.
%t A342768 Table[n^2/FactorInteger[n][[-1,1]],{n,100}] (* _Gus Wiseman_, Aug 09 2021 *)
%o A342768 (PARI) See Links section.
%Y A342768 Cf. A007947, A087019, A342767.
%Y A342768 The sum of prime indices of a(n) is 2*A056239(n) - A061395(n).
%Y A342768 The version for even indices is A129597(n) = 2*a(n) for n > 1.
%Y A342768 The sorted version is A346635.
%Y A342768 These are the positions of first appearances in A346701 and in A346703.
%Y A342768 A001221 counts distinct prime factors.
%Y A342768 A001222 counts prime factors with multiplicity.
%Y A342768 A027193 counts partitions of odd length, ranked by A026424.
%Y A342768 A209281 adds up the odd bisection of standard compositions (even: A346633).
%Y A342768 A346697 adds up the odd bisection of prime indices (reverse: A346699).
%Y A342768 Cf. A000290, A006530, A033942, A037143, A344653, A345957, A346698, A346700, A346704.
%K A342768 nonn
%O A342768 1,2
%A A342768 _Rémy Sigrist_, Apr 02 2021