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A355026
Irregular table read by rows: the n-th row gives the possible values of the number of divisors of numbers with n prime divisors (counted with multiplicity).
3
1, 2, 3, 4, 4, 6, 8, 5, 8, 9, 12, 16, 6, 10, 12, 16, 18, 24, 32, 7, 12, 15, 16, 20, 24, 27, 32, 36, 48, 64, 8, 14, 18, 20, 24, 30, 32, 36, 40, 48, 54, 64, 72, 96, 128, 9, 16, 21, 24, 25, 28, 36, 40, 45, 48, 60, 64, 72, 80, 81, 96, 108, 128, 144, 192, 256
OFFSET
0,2
COMMENTS
First differs from A074139 at the 8th row.
The n-th row begins with n+1, which corresponds to powers of primes, and ends with 2^n, which corresponds to squarefree numbers.
The n-th row contains the distinct values of the n-th row of A238963.
EXAMPLE
Table begins:
1;
2;
3, 4;
4, 6, 8;
5, 8, 9, 12, 16;
6, 10, 12, 16, 18, 24, 32;
7, 12, 15, 16, 20, 24, 27, 32, 36, 48, 64;
8, 14, 18, 20, 24, 30, 32, 36, 40, 48, 54, 64, 72, 96, 128;
...
Numbers k with Omega(k) = 2 are either of the form p^2 with p prime, or of the form p1*p2 with p1 and p2 being distinct primes. The corresponding numbers of divisors are 3 and 4, respectively. Therefore the second row is {3, 4}.
MATHEMATICA
row[n_] := Union[Times @@ (# + 1) & /@ IntegerPartitions[n]]; Array[row, 9, 0] // Flatten
PROG
(PARI) row(n) = { my (m=Map()); forpart(p=n, mapput(m, prod(k=1, #p, 1+p[k]), 0)); Vec(m) } \\ Rémy Sigrist, Jun 17 2022
CROSSREFS
Sequence in context: A325682 A241088 A074139 * A238963 A342940 A331527
KEYWORD
nonn,tabf
AUTHOR
Amiram Eldar, Jun 16 2022
STATUS
approved