A045967 a(1)=4; if n = Product p_i^e_i, n > 1, then a(n) = Product p_{i+1}^{e_i+1}.

4, 9, 25, 27, 49, 225, 121, 81, 125, 441, 169, 675, 289, 1089, 1225, 243, 361, 1125, 529, 1323, 3025, 1521, 841, 2025, 343, 2601, 625, 3267, 961, 11025, 1369, 729, 4225, 3249, 5929, 3375, 1681, 4761, 7225, 3969, 1849, 27225, 2209, 4563, 6125, 7569, 2809, 6075

Offset: 1

Author

N. J. A. Sloane

Keywords

• easy
• nonn
• nice

Comments

If we had a(1) = 1 (instead of 4), then this would be multiplicative and a permutation of the odd powerful numbers (A062739). - Amiram Eldar, Aug 11 2022

References

• From a puzzle proposed by Marc LeBrun.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A045966, A027748, A062739, A124010, A000040.

Cf. A151800.

Programs

Haskell

a045967 1 = 4
a045967 n = product $ zipWith (^)
            (map a151800 $ a027748_row n) (map (+ 1) $ a124010_row n)
-- Reinhard Zumkeller, Jun 03 2013, Dec 23 2011

Mathematica

a[1]=4; a[n_] := Thread[f = FactorInteger[n]; Times @@ Power[f[[All, 1]] // NextPrime , f[[All, 2]] + 1]]; Array[a, 50] (* Jean-François Alcover, Feb 03 2015 *)

Formula

Sum_{n>=1} 1/a(n) = 2*zeta(2)*zeta(3)/(3*zeta(6)) - 3/4. - Amiram Eldar, Aug 11 2022

Extensions

More terms from David W. Wilson