A366993 - OEIS

%I #7 Nov 02 2023 10:26:37

%S 1,1,1,4,1,1,1,8,9,1,1,4,1,1,1,8,1,9,1,4,1,1,1,8,25,1,27,4,1,1,1,32,1,

%T 1,1,36,1,1,1,8,1,1,1,4,9,1,1,8,49,25,1,4,1,27,1,8,1,1,1,4,1,1,9,32,1,

%U 1,1,4,1,1,1,72,1,1,25,4,1,1,1,8,27,1,1,4

%N The largest divisor of n that is a term of A056166.

%C The number of these divisors is A095691(n) and their sum is A366990(n).

%H Amiram Eldar, <a href="/A366993/b366993.txt">Table of n, a(n) for n = 1..10000</a>

%F Multiplicative with a(p) = 1 and a(p^e) = p^A007917(e).

%F a(n) <= n, with equality if and only if n is in A056166.

%F a(n) >= 1, with equality if and only if n is squarefree (A005117).

%t f[p_, e_] := p^If[e == 1, 0, NextPrime[e+1, -1]]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]

%o (PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i, 1]^precprime(f[i, 2]));}

%Y Cf. A005117, A007917, A056166, A095691, A366988, A366990.

%K nonn,easy,mult

%O 1,4

%A _Amiram Eldar_, Oct 31 2023