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

Author

Alford Arnold, Jul 19 2007

Keywords

• tabf
• easy
• nonn

Examples

			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.
		

Crossrefs

Cf. A080577, A131801.

Programs

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

Formula

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

Extensions

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