A045971 a(1)=8; if n = Product p_i^e_i, n > 1, then a(n) = Product p_{i+1}^{e_i+2}.

8, 27, 125, 81, 343, 3375, 1331, 243, 625, 9261, 2197, 10125, 4913, 35937, 42875, 729, 6859, 16875, 12167, 27783, 166375, 59319, 24389, 30375, 2401, 132651, 3125, 107811, 29791, 1157625, 50653, 2187, 274625, 185193, 456533, 50625, 68921, 328509, 614125

Offset: 1

Author

N. J. A. Sloane

Keywords

• easy
• nonn

References

• From a puzzle proposed by Marc LeBrun.

Crossrefs

Cf. A045965, A045966, A045967, A045968, A045969, A045970, A045972, A045973, A065483.

Programs

Mathematica

f[p_, e_] := NextPrime[p]^(e + 2); a[1] = 8; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Sep 19 2023 *)

Formula

Sum_{n>=1} 1/a(n) = (4/5) * A065483 - 7/8 = 0.196827322859... . - Amiram Eldar, Sep 19 2023

Extensions

More terms from David W. Wilson