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a(1)=6; if n = Product p_i^e_i, n>1, then a(n) = Product p_{i+1}^e_i * Product p_{i+2}^e_i.
5

%I #14 Sep 19 2023 01:44:21

%S 6,15,35,225,77,525,143,3375,1225,1155,221,7875,323,2145,2695,50625,

%T 437,18375,667,17325,5005,3315,899,118125,5929,4845,42875,32175,1147,

%U 40425,1517,759375,7735,6555,11011,275625,1763,10005,11305,259875,2021,75075

%N a(1)=6; if n = Product p_i^e_i, n>1, then a(n) = Product p_{i+1}^e_i * Product p_{i+2}^e_i.

%D From a puzzle proposed by _Marc LeBrun_.

%F Sum_{n>=1} 1/a(n) = -5/6 + Product_{k>=2} (1+1/(prime(k)*prime(k+1)-1)) = 0.31383788... . - _Amiram Eldar_, Sep 19 2023

%t f[p_, e_] := (NextPrime[p] * NextPrime[p, 2])^e; a[1] = 6; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Sep 19 2023 *)

%Y Cf. A045965, A045966, A045967, A045968, A045970, A045971, A045972, A045973.

%K easy,nonn

%O 1,1

%A _N. J. A. Sloane_

%E More terms from _David W. Wilson_