A131822 Increment each prime factor for each term of the least prime signature sequence derived from A080577.

1, 3, 9, 15, 27, 45, 105, 81, 135, 225, 315, 1155, 243, 405, 675, 945, 1575, 3465, 15015, 729, 1215, 2025, 2835, 3375, 4725, 10395, 11025, 17325, 45045, 255255, 2187, 3645, 6075, 8505, 10125, 14175, 31185, 23625, 33075, 51975, 135135, 121275, 225225

Offset

1,2

Links

Table of n, a(n) for n=1..43.

Formula

a(n) = A003961(A036035(n-1)). - R. J. Mathar, Nov 11 2007

Example

The term 30 = 2*3*5 becomes 105 = 3*5*7.
From A080577 we obtain
   1
   2
   4,  6
   8, 12, 30
  16, 24, 36, 60, ...
  etc.
so the sequence begins
   1
   3
   9,  15
  27,  45, 105
  81, 135, 225, 315, ...
  etc.

Maple

A003961 := proc(n) local ifs, i ; ifs := ifactors(n)[2] ; mul(nextprime(op(1, i))^op(2, i), i=ifs) ; end: A036042 := proc(n) local a, nredu ; a := 0 ; nredu := n+1 ; while nredu > 0 do nredu := nredu-combinat[numbpart](a) ; a := a+1 ; od: RETURN(a-1) ; end: A036035 := proc(n) local row, idx, pa, a, i ; if n = 0 then 1 ; else row := A036042(n) ; idx := n-add(combinat[numbpart](i), i=0..row-1) ; pa := op(-idx-1, combinat[partition](row)) ; a := 1; for i from 1 to nops(pa) do a := a*ithprime(i)^op(-i, pa) ; od; RETURN(a) ; fi ; end: A131822 := proc(n) A003961(A036035(n-1)) ; end: seq(A131822(n), n=1..80) ; # R. J. Mathar, Nov 11 2007

Crossrefs

Cf. A080577, A131801.

Sequence in context: A147516 A372509 A233819 * A131801 A280963 A122819

Adjacent sequences: A131819 A131820 A131821 * A131823 A131824 A131825

Keyword

tabf,easy,nonn

Author

Alford Arnold, Jul 19 2007

Extensions

Corrected and extended by R. J. Mathar, Nov 11 2007

Status

approved