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 A124010 Triangle in which first row is 0, n-th row (n>1) lists the prime signature of n, that is, the exponents of distinct prime factors in factorization of n. 157
 0, 1, 1, 2, 1, 1, 1, 1, 3, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 4, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 4, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 6, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 3, 2, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS A001222(n)=Sum(T(n,k):1<=k<=A001221(n)); A005361(n)=Product(T(n,k):1<=k<=A001221(n)), n>1; A051903(n)=Max(T(n,k):1<=k<=A001221(n)); A051904(n)=Min(T(n,k):1<=k<=A001221(n)); A067029(n)=T(n,1); A071178(n)=T(n,A001221(n)); A064372(n)=Sum(A064372(T(n,k)):1<=k<=A001221(n)). [Reinhard Zumkeller, Aug 27 2011] Any finite sequence of natural numbers appears as consecutive terms. [Paul Tek, Apr 27 2013] For n > 1: n-th row = n-th row of A067255 without zeros. - Reinhard Zumkeller, Jun 11 2013 LINKS Reinhard Zumkeller, Rows n = 1..10000 of triangle, flattened FORMULA n = Product_k A027748(n,k)^a(n,k). EXAMPLE Initial values of exponents are: 1, [0] 2, [1] 3, [1] 4, [2] 5, [1] 6, [1, 1] 7, [1] 8, [3] 9, [2] 10, [1, 1] 11, [1] 12, [2, 1] 13, [1] 14, [1, 1] 15, [1, 1] 16, [4] 17, [1] 18, [1, 2] 19, [1] 20, [2, 1] ... MAPLE expts:=proc(n) local t1, t2, t3, t4, i; if n=1 then RETURN([0]); fi; if isprime(n) then RETURN([1]); fi; t1:=ifactor(n); if nops(factorset(n))=1 then RETURN([op(2, t1)]); fi; t2:=nops(t1); t3:=[]; for i from 1 to t2 do t4:=op(i, t1); if nops(t4) = 1 then t3:=[op(t3), 1]; else t3:=[op(t3), op(2, t4)]; fi; od; RETURN(t3); end; # N. J. A. Sloane, Dec 20 2007 MATHEMATICA row[1] = {0}; row[n_] := FactorInteger[n][[All, 2]] // Flatten; Table[row[n], {n, 1, 80}] // Flatten (* Jean-François Alcover, Aug 19 2013 *) PROG (Haskell) a124010 n k = a124010_tabf !! (n-1) !! (k-1) a124010_row 1 = [0] a124010_row n = f n a000040_list where    f 1 _      = []    f u (p:ps) = h u 0 where      h v e | m == 0 = h v' (e + 1)            | m /= 0 = if e > 0 then e : f v ps else f v ps            where (v', m) = divMod v p a124010_tabf = map a124010_row [1..] -- Reinhard Zumkeller, Jun 12 2013, Aug 27 2011 (PARI) print1(0); for(n=2, 50, f=factor(n)[, 2]; for(i=1, #f, print1(", "f[i]))) \\ Charles R Greathouse IV, Nov 07 2014 (Python) from sympy import factorint def a(n):     f=factorint(n)     return [0] if n==1 else [f[i] for i in f] for n in xrange(1, 21): print a(n) # Indranil Ghosh, May 16 2017 CROSSREFS Cf. A027748, A001221 (row lengths, n>1), A001222 (row sums), A027746, A020639, A064372. Sorted rows: A118914, A212171. Sequence in context: A030358 A118914 A135063 * A212171 A196228 A133364 Adjacent sequences:  A124007 A124008 A124009 * A124011 A124012 A124013 KEYWORD easy,nonn,tabf AUTHOR Franklin T. Adams-Watters, Nov 01 2006 STATUS approved

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Last modified February 17 17:27 EST 2018. Contains 299296 sequences. (Running on oeis4.)