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A131822 Increment each prime factor for each term of the least prime signature sequence derived from A080577. 4
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 (list; graph; refs; listen; history; text; internal format)
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: A339886 A147516 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

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Last modified June 21 10:09 EDT 2021. Contains 345360 sequences. (Running on oeis4.)