A200746 Completely multiplicative function with a(prime(k)) = prime(k)*prime(k-1), a(2) = 2.

1, 2, 6, 4, 15, 12, 35, 8, 36, 30, 77, 24, 143, 70, 90, 16, 221, 72, 323, 60, 210, 154, 437, 48, 225, 286, 216, 140, 667, 180, 899, 32, 462, 442, 525, 144, 1147, 646, 858, 120, 1517, 420, 1763, 308, 540, 874, 2021, 96, 1225, 450, 1326, 572, 2491, 432, 1155, 280, 1938

Offset: 1

Author

Franklin T. Adams-Watters, Nov 25 2011

Keywords

• nonn
• mult
• look

Links

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

Crossrefs

Cf. A064989, A108951, A191002.

Programs

Mathematica

a200746[n_Integer] := Block[{f, p, a},
  f[x_] := Transpose@FactorInteger[x];
  p[x_] := Which[
    x == 1, 1,
    x == 2, 2,
    True, x NextPrime[x, -1]];
  a[x_] := Times @@ Power[p /@ First[f[x]], Last[f[x]]];
a /@ Range[n]]; a200746[57] (* Michael De Vlieger, Dec 19 2014 *)

PARI

a(n)=local(fm=factor(n));prod(k=1,matsize(fm)[1],(fm[k,1]*if(fm[k,1]==2,1,precprime(fm[k,1]-1)))^fm[k,2])

Scheme

;; With memoization-macro definec.
(definec (A200746 n) (if (<= n 2) n (* n (A064989 n)))) ;; Antti Karttunen, Dec 18 2014

Formula

a(n) = n * A064989(n).

Sum_{n>=1} 1/a(n) = 2/Product_{k>=1} (1 - 1/(prime(k)*prime(k+1))) = 2.75321091... . - Amiram Eldar, Jan 07 2023