A129597 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

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

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)

MATHEMATICA

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

PROG

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

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.

Sequence in context: A333140 A141042 A123667 * A088843 A154784 A328709

Adjacent sequences: A129594 A129595 A129596 * A129598 A129599 A129600

KEYWORD

nonn

AUTHOR

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

STATUS

approved