%I #18 Oct 23 2021 00:32:11

%S 1,4,6,16,10,24,14,64,54,40,22,96,26,56,90,256,34,216,38,160,126,88,

%T 46,384,250,104,486,224,58,360,62,1024,198,136,350,864,74,152,234,640,

%U 82,504,86,352,810,184,94,1536,686,1000,306,416,106,1944,550,896,342

%N Central diagonal of array A129595.

%C These are the positions of first appearances of each positive integer in A346704. - _Gus Wiseman_, Oct 16 2021

%H Antti Karttunen, <a href="/A129597/b129597.txt">Table of n, a(n) for n = 1..10000</a>

%F From _Gus Wiseman_, Aug 10 2021: (Start)

%F For n > 1, A001221(a(n)) = A099812(n).

%F If g = A006530(n) is the greatest prime factor of n > 1, then a(n) = 2n^2/g.

%F a(n) = A100484(A000720(n)) = 2n iff n is prime.

%F a(n > 1) = 2*A342768(n).

%F (End)

%t Table[If[n==1,1,2*n^2/FactorInteger[n][[-1,1]]],{n,100}] (* _Gus Wiseman_, Aug 10 2021 *)

%o (PARI) A129597(n) = if(1==n, n, my(f=factor(n)); (2*n*n)/f[#f~, 1]); \\ _Antti Karttunen_, Oct 16 2021

%Y a(n) = A129595(n,n).

%Y The sum of prime indices of a(n) is 2*A056239(n) - A061395(n) + 1 for n > 1.

%Y The version for odd indices is A342768(n) = a(n)/2 for n > 1.

%Y Except the first term, the sorted version is 2*A346635.

%Y These are the positions of first appearances in A346704.

%Y A001221 counts distinct prime factors.

%Y A001222 counts prime factors with multiplicity.

%Y A027187 counts partitions of even length, ranked by A028260.

%Y A346633 adds up the even bisection of standard compositions (odd: A209281).

%Y A346698 adds up the even bisection of prime indices (reverse: A346699).

%Y Cf. A000290, A006530, A037143, A329888, A344606, A345957, A346697, A346700, A346701.

%K nonn

%O 1,2

%A _Antti Karttunen_, May 01 2007, based on _Marc LeBrun_'s Jan 11 2006 message on SeqFan mailing list.