A368911 - OEIS

%I #16 Feb 07 2024 14:31:52

%S 0,8,119,1282,13259,133700,1341168,13432710,134458668,1345577839

%N Number of terms of A327934 less than 10^n, where A327934 gives numbers k such that there is no prime p such that p^p divides k, but for its arithmetic derivative a positive finite number of such primes exist.

%C Also number of terms of A327934 in range [1 .. 10^n] because for all k >= 0, A360111(10^k) = 0.

%C Value a(n) / 10^n converges towards the asymptotic mean of A360111. See comments there and in A368919.

%F a(n) = Sum_{k=1..10^n} A360111(k).

%o (PARI)

%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

%o A359550(n) = { my(f = factor(n)); prod(k=1, #f~, (f[k, 2]<f[k, 1])); };

%o A360111(n) = ((n>1)&&A359550(n)&&!A359550(A003415(n)));

%o tp=10; s=0; for(n=1,10^10,s+=A360111(n); if(1+n==tp,print1(s,", "),if(n==tp, tp *= 10)));

%Y Cf. A003415, A327934, A360111, A368919, A368920.

%K nonn,more

%O 1,2

%A _Antti Karttunen_, Jan 14 2024

%E a(9)-a(10) from _Antti Karttunen_, Jan 31 2024