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