A129597 Central diagonal of array A129595.

1, 4, 6, 16, 10, 24, 14, 64, 54, 40, 22, 96, 26, 56, 90, 256, 34, 216, 38, 160, 126, 88, 46, 384, 250, 104, 486, 224, 58, 360, 62, 1024, 198, 136, 350, 864, 74, 152, 234, 640, 82, 504, 86, 352, 810, 184, 94, 1536, 686, 1000, 306, 416, 106, 1944, 550, 896, 342

Offset: 1

Author

Antti Karttunen, May 01 2007, based on Marc LeBrun's Jan 11 2006 message on SeqFan mailing list

Keywords

• nonn

Comments

These are the positions of first appearances of each positive integer in A346704. - Gus Wiseman, Oct 16 2021

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

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

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

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

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

These are the positions of first appearances in A346704.

A001221 counts distinct prime factors.

A001222 counts prime factors with multiplicity.

A027187 counts partitions of even length, ranked by A028260.

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

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

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

Programs

Mathematica

Table[If[n==1,1,2*n^2/FactorInteger[n][[-1,1]]],{n,100}] (* Gus Wiseman, Aug 10 2021 *)

PARI

A129597(n) = if(1==n, n, my(f=factor(n)); (2*n*n)/f[#f~, 1]); \\ Antti Karttunen, Oct 16 2021

Formula

From Gus Wiseman, Aug 10 2021: (Start)

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

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

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

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

(End)