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

Author

Antti Karttunen, Jan 02 2024

Keywords

• nonn

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.

Crossrefs

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

Permutation of A366377.

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).