A377983 a(n) is the number of terms in the range of A276087 that are <= n, where A276087(n) = A276086(A276086(n)) [the twofold application of the primorial base exp-function].

0, 0, 1, 2, 2, 3, 4, 5, 5, 5, 6, 7, 7, 8, 9, 9, 9, 10, 11, 12, 12, 12, 13, 14, 14, 14, 15, 15, 15, 16, 17, 18, 18, 18, 19, 19, 19, 20, 21, 21, 21, 22, 23, 24, 24, 25, 26, 27, 27, 27, 28, 28, 28, 29, 29, 29, 29, 29, 30, 31, 31, 32, 33, 34, 34, 34, 35, 36, 36, 36, 37, 38, 38, 39, 40, 41, 41, 41, 42, 43, 43, 43, 44, 45

Offset: 0

Author

Antti Karttunen, Nov 13 2024

Keywords

• nonn

Comments

The number of terms of A377871 that are less than or equal to n.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..100000

Crossrefs

Partial sums of A377870.

Cf. A276085, A276087, A359550, A377871.

Cf. also A377982.

Programs

PARI

up_to = 10000;
A359550(n) = { my(pp); forprime(p=2, , pp = p^p; if(!(n%pp), return(0)); if(pp > n, return(1))); };
A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*prod(i=1,primepi(f[k, 1]-1),prime(i))); };
A377870(n) = (isprime(n) || (A359550(n) && A359550(A276085(n))));
A377983list(up_to) = { my(v=vector(1+up_to), s=0); v[1] = s = A377870(0); for(n=1,up_to,s += A377870(n); v[1+n] = s); (v); };
v377983 = A377983list(up_to);
A377983(n) = v377983[1+n];

Formula

a(n) = Sum_{i=1..n} A377870(i) = Sum_{i=1..n} A359550(i) * A359550(A276085(i)).