login
A336870
Irregular triangle read by rows where T(n,k) is the number of divisors d of the superprimorial A006939(n) with k prime factors (counting multiplicity), such that d and A006939(n)/d both have distinct prime multiplicities.
3
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 4, 4, 2, 4, 4, 1, 1, 1, 1, 1, 1, 4, 4, 7, 7, 7, 7, 7, 7, 4, 4, 1, 1, 1, 1, 1, 1, 4, 4, 7, 18, 10, 10, 15, 21, 21, 15, 10, 10, 18, 7, 4, 4, 1, 1, 1, 1, 1, 1, 4, 4, 7, 18, 23, 15, 20, 37, 35, 40, 46, 32, 46, 40, 35, 37, 20, 15, 23, 18, 7, 4, 4, 1, 1, 1
OFFSET
0,11
COMMENTS
Are there any zeros (cf. A336939)?
A number has distinct prime multiplicities iff its prime signature is strict.
EXAMPLE
Triangle begins:
1
1 1
1 1 1 1
1 1 1 4 1 1 1
1 1 1 4 4 2 4 4 1 1 1
1 1 1 4 4 7 7 7 7 7 7 4 4 1 1 1
Row n = 4 counts the following divisors:
1 7 25 27 16 112 400 432 3024 10800 75600
63 54 675 1350 1008
75 56 1400 1200
175 189 4725 2800
MATHEMATICA
chern[n_]:=Product[Prime[i]^(n-i+1), {i, n}];
Table[Length[Select[Divisors[chern[n]], UnsameQ@@Last/@FactorInteger[#]&&UnsameQ@@Last/@FactorInteger[chern[n]/#]&&PrimeOmega[#]==k&]], {n, 0, 6}, {k, 0, PrimeOmega[chern[n]]}]
CROSSREFS
A000124 gives row lengths.
A336419 gives row sums.
A336500 is the generalization to all positive integers.
A336939 is the version for factorials.
A000005 counts divisors.
A000110 counts divisors of superprimorials with distinct prime multiplicities.
A000142 lists factorials.
A000325 counts divisors of superprimorials with equal prime multiplicities.
A006939 lists superprimorials.
A130091 lists numbers with distinct prime multiplicities.
A181796 counts divisors with distinct prime multiplicities.
A327498 gives the maximum divisor of n with distinct prime multiplicities.
A336423 counts chains using A130091.
Sequence in context: A366145 A204160 A360165 * A184101 A347176 A164561
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, Aug 08 2020
STATUS
approved