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A368911
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.
3
0, 8, 119, 1282, 13259, 133700, 1341168, 13432710, 134458668, 1345577839
OFFSET
1,2
COMMENTS
Also number of terms of A327934 in range [1 .. 10^n] because for all k >= 0, A360111(10^k) = 0.
Value a(n) / 10^n converges towards the asymptotic mean of A360111. See comments there and in A368919.
FORMULA
a(n) = Sum_{k=1..10^n} A360111(k).
PROG
(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A359550(n) = { my(f = factor(n)); prod(k=1, #f~, (f[k, 2]<f[k, 1])); };
A360111(n) = ((n>1)&&A359550(n)&&!A359550(A003415(n)));
tp=10; s=0; for(n=1, 10^10, s+=A360111(n); if(1+n==tp, print1(s, ", "), if(n==tp, tp *= 10)));
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Antti Karttunen, Jan 14 2024
EXTENSIONS
a(9)-a(10) from Antti Karttunen, Jan 31 2024
STATUS
approved