cp's OEIS Frontend

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

%I A355538 #9 Jul 07 2024 19:12:53
%S A355538 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,
%T A355538 14,14,15,16,17,18,18,19,20,21,21,23,23,24,25,26,26,27,27,28,29,30,30,
%U A355538 31,32,33,34,35,35,37,37,38,39,39,40,42,42,43,44,46,46
%N A355538 Partial sum of A001221 (number of distinct prime factors) minus 1, ranging from 2 to n.
%C A355538 For initial terms up to 30 we have a(n) = Log_2 A355537(n).
%F A355538 a(n) = A013939(n) - n + 1.
%t A355538 Table[Total[(PrimeNu[#]-1)&/@Range[2,n]],{n,1,100}]
%Y A355538 The sum of the same range is A000096.
%Y A355538 The product of the same range is A000142, Heinz number A070826.
%Y A355538 For divisors (not just prime factors) we get A002541, also A006218, A077597.
%Y A355538 A shifted variation is A013939.
%Y A355538 The unshifted version is A022559, product A327486, w/o multiplicity A355537.
%Y A355538 The ranges themselves are the rows of A131818 (shifted).
%Y A355538 Partial sums of A297155 (shifted).
%Y A355538 A001221 counts distinct prime factors, with sum A001414.
%Y A355538 A001222 counts prime factors with multiplicity.
%Y A355538 A003963 multiplies together the prime indices of n.
%Y A355538 A056239 adds up prime indices, row sums of A112798.
%Y A355538 A066843 gives partial sums of A000005.
%Y A355538 Cf. A000720, A002110, A076610, A305054, A355538, A355731, A355733, A355741, A355744, A355745, A355746, A355747.
%K A355538 nonn
%O A355538 1,10
%A A355538 _Gus Wiseman_, Jul 23 2022