The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A333175 If n = Product (p_j^k_j) then a(n) = Sum (a(n/p_j^k_j)), with a(1) = 1. 16
 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 6, 1, 1, 2, 2, 2, 2, 1, 2, 2, 2, 1, 6, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 6, 1, 2, 2, 1, 2, 6, 1, 2, 2, 6, 1, 2, 1, 2, 2, 2, 2, 6, 1, 2, 1, 2, 1, 6, 2, 2, 2, 2, 1, 6, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS Number of ordered prime factorizations of radical of n. Number of permutations of the prime indices of n (counting multiplicity) avoiding the patterns (1,2,1) and (2,1,2). These are permutations with all equal parts contiguous. Depends only on sorted prime signature (A118914). - Gus Wiseman, Jun 27 2020 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 Wikipedia, Permutation pattern FORMULA a(1) = 1; a(n) = Sum_{d|n, d < n, gcd(d, n/d) = 1} A069513(n/d) * a(d). a(n) = A000142(A001221(n)). EXAMPLE From Gus Wiseman, Jun 27 2020 (Start) The a(n) permutations of prime indices for n = 2, 12, 60:   (1)  (112)  (1123)        (211)  (1132)               (2113)               (2311)               (3112)               (3211) (End) MAPLE f:= n -> nops(numtheory:-factorset(n))!: map(f, [\$1..100]); # Robert Israel, Mar 12 2020 MATHEMATICA a[1] = 1; a[n_] := a[n] = Plus @@ (a[n/#[[1]]^#[[2]]] & /@ FactorInteger[n]); Table[a[n], {n, 1, 100}] a[1] = 1; a[n_] := a[n] = Sum[If[GCD[n/d, d] == 1 && d < n, Boole[PrimePowerQ[n/d]] a[d], 0], {d, Divisors[n]}]; Table[a[n], {n, 1, 100}] Table[PrimeNu[n]!, {n, 1, 100}] CROSSREFS Cf. A000142, A000961 (positions of 1's), A001221, A050363, A066504, A069513, A064372, A093320, A292586. Dominates A335451. Permutations of prime indices are A008480. Unsorted prime signature is A124010. Sorted prime signature is A118914. (1,2,1)-avoiding permutations of prime indices are A335449. (2,1,2)-avoiding permutations of prime indices are A335450. (1,2,1) or (2,1,2)-matching permutations of prime indices are A335460. (1,2,1) and (2,1,2)-matching permutations of prime indices are A335462. Cf. A056239, A112798, A181796, A333221, A335452, A335463, A335521. Sequence in context: A339887 A259936 A050320 * A294893 A336570 A121382 Adjacent sequences:  A333172 A333173 A333174 * A333176 A333177 A333178 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Mar 11 2020 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 1 00:13 EDT 2021. Contains 346377 sequences. (Running on oeis4.)