A380088 - OEIS

%I #8 Jan 12 2025 03:53:28

%S 1,2,3,4,5,6,7,1,9,10,11,12,13,14,15,1,17,18,19,20,21,22,23,3,25,26,

%T 27,28,29,30,31,1,33,34,35,36,37,38,39,5,41,42,43,44,45,46,47,3,49,50,

%U 51,52,53,54,55,7,57,58,59,60,61,62,63,1,65,66,67,68,69,70

%N The largest unitary divisor of n that is a term in A207481.

%H Amiram Eldar, <a href="/A380088/b380088.txt">Table of n, a(n) for n = 1..10000</a>

%F Multiplicative with a(p^e) = p^e if e <= p, and 1 otherwise.

%F a(n) = 1 if and only if n is in A054743.

%F a(n) < n if and only if n is in A185359.

%F a(n) = n if and only if n is in A207481.

%F Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = Product_{p prime} (p^(2*(p+1)) + p^(2*p+1) - p^(p+1) - p^p + 1)/(p^(2*p+1) * (p+1)) = 0.87453068804586281444... .

%t f[p_, e_] := If[e <= p, p^e, 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~, if(f[i, 2] <= f[i, 1], f[i, 1]^f[i, 2], 1));}

%Y Cf. A005117, A054743, A077610, A185359, A207481, A377518, A380085, A380089, A380090.

%K nonn,easy,mult

%O 1,2

%A _Amiram Eldar_, Jan 12 2025