A036491 Transformation of A036490: 5^a*7^b*11^c -> 5^a*7^floor((b+2)/2)*11^c.

5, 7, 11, 25, 35, 49, 55, 77, 121, 125, 175, 245, 275, 49, 385, 539, 605, 625, 847, 875, 1225, 1331, 1375, 245, 1925, 343, 2695, 3025, 3125, 539, 4235, 4375, 5929, 6125, 6655, 6875, 1225, 9317, 9625, 1715, 13475, 14641, 15125, 15625, 343, 2695, 21175

Offset: 1

Author

Olivier Gérard

Keywords

• nonn
• easy
• look

References

• G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 160.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A036490, A036492.

Programs

Haskell

a036491 n = f z z where
   f x y | x `mod` 2401 == 0 = f (x `div` 49) (y `div` 7)
         | x `mod` 343 == 0  = y `div` 7
         | otherwise         = y
   z = a036490 n
-- Reinhard Zumkeller, Feb 19 2013

Mathematica

f[pp_(*primes*), max_(*maximum term*)] := Module[{a, aa, k, iter}, k = Length[pp]; aa = Array[a, k]; iter = Table[{a[j], 0, PowerExpand @ Log[pp[[j]], max/Times @@ (Take[pp, j-1]^Take[aa, j-1])]}, {j, 1, k}]; Table[Times @@ (pp^aa), Sequence @@ iter // Evaluate] // Flatten // Sort]; A036490 = f[{5, 7, 11}, 2*10^14] // Rest; a[n_] := (a0 = A036490[[n]]; b = Max[1, IntegerExponent[a0, 7]]; 7^(Floor[(b+2)/2]-b) * a0); Table[a[n], {n, 1, Length[A036490]}]; (* Jean-François Alcover, Sep 19 2012, updated Nov 12 2016 *)

Extensions

Offset corrected by Reinhard Zumkeller, Feb 19 2013