A131822 - OEIS

%I #13 Feb 20 2019 05:34:16

%S 1,3,9,15,27,45,105,81,135,225,315,1155,243,405,675,945,1575,3465,

%T 15015,729,1215,2025,2835,3375,4725,10395,11025,17325,45045,255255,

%U 2187,3645,6075,8505,10125,14175,31185,23625,33075,51975,135135,121275,225225

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

%F a(n) = A003961(A036035(n-1)). - _R. J. Mathar_, Nov 11 2007

%e The term 30 = 2*3*5 becomes 105 = 3*5*7.

%e From A080577 we obtain

%e    1

%e    2

%e    4,  6

%e    8, 12, 30

%e   16, 24, 36, 60, ...

%e   etc.

%e so the sequence begins

%e    1

%e    3

%e    9,  15

%e   27,  45, 105

%e   81, 135, 225, 315, ...

%e   etc.

%p 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

%Y Cf. A080577, A131801.

%K tabf,easy,nonn

%O 1,2

%A _Alford Arnold_, Jul 19 2007

%E Corrected and extended by _R. J. Mathar_, Nov 11 2007