A339823 a(n) = A056239(n) - A000523(n).

0, 0, 1, 0, 1, 1, 2, 0, 1, 1, 2, 1, 3, 2, 2, 0, 3, 1, 4, 1, 2, 2, 5, 1, 2, 3, 2, 2, 6, 2, 7, 0, 2, 3, 2, 1, 7, 4, 3, 1, 8, 2, 9, 2, 2, 5, 10, 1, 3, 2, 4, 3, 11, 2, 3, 2, 5, 6, 12, 2, 13, 7, 3, 0, 3, 2, 13, 3, 5, 2, 14, 1, 15, 7, 2, 4, 3, 3, 16, 1, 2, 8, 17, 2, 4, 9, 6, 2, 18, 2, 4, 5, 7, 10, 5, 1, 19, 3, 3, 2, 20, 4, 21, 3, 3

Offset: 1

Author

Antti Karttunen, Dec 18 2020

Keywords

• nonn

Comments

a(n) is the difference at n between the value of a PrimePi-based pseudo-logarithmic function (A056239) and log_2 floored down (A000523).

All terms are nonnegative. (Cf. Bertrand's postulate).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65536
• Wikipedia, Bertrand's postulate
• Index entries for sequences related to binary expansion of n
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A000523, A056239.

Programs

PARI

A000523(n) = if( n<1, 0, #binary(n) - 1); \\ From A000523
A056239(n) = { my(f); if(1==n, 0, f=factor(n); sum(i=1, #f~, f[i,2] * primepi(f[i,1]))); }
A339823(n) = A056239(n)-A000523(n);

Formula

a(n) = A056239(n) - A000523(n).