A368918 a(n) is the number of integers m in the range 0..n such that the arithmetic derivative of A276086(m) has no divisors of the form p^p.

0, 1, 2, 3, 4, 5, 6, 7, 7, 8, 9, 10, 11, 12, 13, 14, 14, 15, 16, 17, 18, 19, 20, 21, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 32, 33, 34, 35, 36, 37, 38, 39, 39, 40, 41, 42, 43, 44, 45, 46, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 57, 58, 59, 60, 61, 62, 63, 64, 64, 65, 66, 67, 68, 69, 70, 71, 71, 72

Offset

0,3

Links

Antti Karttunen, Table of n, a(n) for n = 0..65537

Index entries for sequences related to primorial base

Formula

a(0) = 0, for n > 0, a(n) = a(n-1) + A368916(n) = a(n-1) + A359550(A327860(n)).

For all n >= 1, a(A368917(n)) = n.

For all n >= 0, a(n) >= A328307(n) - 1.

Prog

(PARI)
up_to = 65537;
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A359550(n) = { my(f = factor(n)); prod(k=1, #f~, (f[k, 2]<f[k, 1])); };
A368916(n) = { my(u=A276086(n)); ((u>1)&&A359550(A003415(u))); };
A368918list(up_to) = { my(v=vector(up_to), s=A368916(0)); for(i=1, up_to, s +=
A368916(i); v[i] = s); (v); };
v368918 = A368918list(up_to);
A368918(n) = if(!n, 0, v368918[n]);

Crossrefs

Partial sums of A368916.

Left inverse of A368917.

Cf. A003415, A276086, A327860, A328307, A359550.

Sequence in context: A053759 A060431 A228298 * A309082 A124808 A238401

Adjacent sequences: A368915 A368916 A368917 * A368919 A368920 A368921

Keyword

nonn

Author

Antti Karttunen, Jan 10 2024

Status

approved