login
Completely multiplicative function with a(prime(k)) = prime(k)*prime(k+1).
11

%I #28 Jan 07 2023 04:00:33

%S 1,6,15,36,35,90,77,216,225,210,143,540,221,462,525,1296,323,1350,437,

%T 1260,1155,858,667,3240,1225,1326,3375,2772,899,3150,1147,7776,2145,

%U 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

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

%H Amiram Eldar, <a href="/A191002/b191002.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Di#divseq">Index to divisibility sequences</a>.

%F a(n) = n * A003961(n). - _Franklin T. Adams-Watters_, Nov 25 2011

%F Sum_{n>=1} 1/a(n) = 1/Product_{k>=1} (1 - 1/(prime(k)*prime(k+1))) = 1.37660546... . - _Amiram Eldar_, Jan 07 2023

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

%o (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])

%Y Cf. A003961, A200746.

%K nonn,mult

%O 1,2

%A _Franklin T. Adams-Watters_, Jun 16 2011