A191002 Completely multiplicative function with a(prime(k)) = prime(k)*prime(k+1).

1, 6, 15, 36, 35, 90, 77, 216, 225, 210, 143, 540, 221, 462, 525, 1296, 323, 1350, 437, 1260, 1155, 858, 667, 3240, 1225, 1326, 3375, 2772, 899, 3150, 1147, 7776, 2145, 1938, 2695, 8100, 1517, 2622, 3315, 7560, 1763, 6930, 2021, 5148, 7875, 4002, 2491, 19440, 5929, 7350, 4845, 7956, 3127, 20250, 5005, 16632, 6555, 5394, 3599, 18900

Offset: 1

Author

Franklin T. Adams-Watters, Jun 16 2011

Keywords

• nonn
• mult

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Index to divisibility sequences.

Crossrefs

Cf. A003961, A200746.

Programs

Mathematica

f[p_, e_] := (p * NextPrime[p])^(e); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Aug 04 2022 *)

PARI

a(n)=local(fm);fm=factor(n);prod(k=1,matsize(fm)[1],(fm[k,1]*nextprime(fm[k,1]+1))^fm[k,2])

Formula

a(n) = n * A003961(n). - Franklin T. Adams-Watters, Nov 25 2011

Sum_{n>=1} 1/a(n) = 1/Product_{k>=1} (1 - 1/(prime(k)*prime(k+1))) = 1.37660546... . - Amiram Eldar, Jan 07 2023