A366884 Number of branching factorizations of the least integer of each prime signature (A025487).

0, 1, 2, 3, 5, 11, 15, 45, 19, 51, 62, 195, 113, 188, 345, 873, 645, 731, 1890, 911, 3989, 207, 2405, 3585, 2950, 10221, 6525, 18483, 1709, 15775, 19569, 12235, 54718, 43545, 86515, 12405, 99215, 9332, 105447, 51822, 55885, 290611, 17753, 120075, 277203, 408105, 83505, 605135, 80565, 562739, 223191, 432975, 1533670

Offset

1,3

Comments

Sequence appears to be injective, but can it be proved? This would prove also the conjectures given in A277120 and A366377.

Of the first 21001 terms, there are 701 terms ending with digit "0", 614 with "1", 68 with "2", 570 with "3", 0 with "4", 17795 with "5", 0 with "6", 550 with "7", 67 with "8", and 636 with "9". Why such an overrepresentation (~ 85% of the total) of the terms of form 10k+5? Do any terms of the form 10k+4 or 10k+6 exist? See also the comments in A052886.

Links

Antti Karttunen, Table of n, a(n) for n = 1..21001

Michael De Vlieger, Plot k = a(n) mod 10 at (x,y) = (n mod 144, 1 + floor(n/144)), n = 1..20736, showing 0 in black, 1 in red, 2 in orange, 3 in yellow, 4 = dark green, 5 = bright green, 6 = cyan, 7 = light blue, 8 = dark blue, and 9 in purple.

Formula

a(n) = A277120(A025487(n)).

a(n) = A366377(A181815(n)).

For all n >= 1, a(A025488(n)) = A007317(n), a(A098719(n)) = A052886(n).

Crossrefs

Cf. A007317, A025487, A025488, A052886, A098719, A181815, A277120.

Permutation of A366377.

Sequence in context: A230147 A324855 A316467 * A282238 A004690 A001882

Adjacent sequences: A366881 A366882 A366883 * A366885 A366886 A366887

Keyword

nonn

Author

Antti Karttunen, Jan 02 2024

Status

approved