Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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