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

%I A131822 #13 Feb 20 2019 05:34:16
%S A131822 1,3,9,15,27,45,105,81,135,225,315,1155,243,405,675,945,1575,3465,
%T A131822 15015,729,1215,2025,2835,3375,4725,10395,11025,17325,45045,255255,
%U A131822 2187,3645,6075,8505,10125,14175,31185,23625,33075,51975,135135,121275,225225
%N A131822 Increment each prime factor for each term of the least prime signature sequence derived from A080577.
%F A131822 a(n) = A003961(A036035(n-1)). - _R. J. Mathar_, Nov 11 2007
%e A131822 The term 30 = 2*3*5 becomes 105 = 3*5*7.
%e A131822 From A080577 we obtain
%e A131822    1
%e A131822    2
%e A131822    4,  6
%e A131822    8, 12, 30
%e A131822   16, 24, 36, 60, ...
%e A131822   etc.
%e A131822 so the sequence begins
%e A131822    1
%e A131822    3
%e A131822    9,  15
%e A131822   27,  45, 105
%e A131822   81, 135, 225, 315, ...
%e A131822   etc.
%p A131822 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 A131822 Cf. A080577, A131801.
%K A131822 tabf,easy,nonn
%O A131822 1,2
%A A131822 _Alford Arnold_, Jul 19 2007
%E A131822 Corrected and extended by _R. J. Mathar_, Nov 11 2007