A355538 Partial sum of A001221 (number of distinct prime factors) minus 1, ranging from 2 to n.

0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 3, 3, 4, 5, 5, 5, 6, 6, 7, 8, 9, 9, 10, 10, 11, 11, 12, 12, 14, 14, 14, 15, 16, 17, 18, 18, 19, 20, 21, 21, 23, 23, 24, 25, 26, 26, 27, 27, 28, 29, 30, 30, 31, 32, 33, 34, 35, 35, 37, 37, 38, 39, 39, 40, 42, 42, 43, 44, 46, 46

Offset: 1

Author

Gus Wiseman, Jul 23 2022

Keywords

• nonn

Comments

For initial terms up to 30 we have a(n) = Log_2 A355537(n).

Crossrefs

The sum of the same range is A000096.

The product of the same range is A000142, Heinz number A070826.

For divisors (not just prime factors) we get A002541, also A006218, A077597.

A shifted variation is A013939.

The unshifted version is A022559, product A327486, w/o multiplicity A355537.

The ranges themselves are the rows of A131818 (shifted).

Partial sums of A297155 (shifted).

A001221 counts distinct prime factors, with sum A001414.

A001222 counts prime factors with multiplicity.

A003963 multiplies together the prime indices of n.

A056239 adds up prime indices, row sums of A112798.

A066843 gives partial sums of A000005.

Cf. A000720, A002110, A076610, A305054, A355538, A355731, A355733, A355741, A355744, A355745, A355746, A355747.

Programs

Mathematica

Table[Total[(PrimeNu[#]-1)&/@Range[2,n]],{n,1,100}]

Formula

a(n) = A013939(n) - n + 1.