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A355029 Irregular table read by rows: the n-th row gives the possible values of the number of prime divisors (counted with multiplicity) of numbers with n divisors.

%I A355029 #12 Jul 04 2025 03:08:30
%S A355029 0,1,2,2,3,4,3,5,6,3,4,7,4,8,5,9,10,4,5,6,11,12,7,13,6,14,4,5,6,8,15,
%T A355029 16,5,7,9,17,18,6,7,10,19,8,20,11,21,22,5,6,7,8,9,12,23,8,24,13,25,6,
%U A355029 10,26,8,9,14,27,28,7,9,11,15,29,30,5,6,7,9,10,16,31
%N A355029 Irregular table read by rows: the n-th row gives the possible values of the number of prime divisors (counted with multiplicity) of numbers with n divisors.
%C A355029 The n-th row begins with A059975(n) and ends with n-1.
%H A355029 Amiram Eldar, <a href="/A355029/b355029.txt">Table of n, a(n) for n = 1..6758</a> (rows 1..1000, flattened)
%e A355029 Table begins:
%e A355029   0;
%e A355029   1;
%e A355029   2;
%e A355029   2, 3;
%e A355029   4;
%e A355029   3, 5;
%e A355029   6;
%e A355029   3, 4, 7;
%e A355029   4, 8;
%e A355029   5, 9;
%e A355029   ...
%e A355029 Numbers k with 4 divisors are either of the form p1 * p2 with p1 and p2 being distinct primes, or of the form p^3 with p prime. The corresponding numbers of prime divisors (counted with multiplicity) are 2 and 3, respectively. Therefore, the 4th row is {2, 3}.
%t A355029 Table[Union[Total[#-1]& /@ f[n]], {n, 1, 32}] // Flatten (* using the function f by _T. D. Noe_ at A162247 *)
%Y A355029 Cf. A000005, A001222, A059975, A118914, A162247, A355026, A355030 (row lengths).
%K A355029 nonn,tabf
%O A355029 1,3
%A A355029 _Amiram Eldar_, Jun 16 2022