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!)
 A325660 Number of ones in the q-signature of n. 6
 0, 1, 2, 0, 3, 1, 1, 0, 0, 2, 4, 1, 2, 1, 1, 0, 2, 0, 1, 2, 2, 3, 1, 1, 0, 2, 0, 1, 3, 1, 5, 0, 2, 2, 3, 0, 2, 1, 1, 2, 3, 2, 2, 3, 1, 1, 2, 1, 0, 0, 3, 2, 1, 0, 1, 1, 2, 3, 3, 1, 1, 4, 1, 0, 2, 2, 2, 2, 1, 3, 3, 0, 3, 2, 0, 1, 4, 1, 4, 2, 0, 3, 2, 2, 4, 2, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Every positive integer has a unique q-factorization (encoded by A324924) into factors q(i) = prime(i)/i, i > 0. For example:    11 = q(1) q(2) q(3) q(5)    50 = q(1)^3 q(2)^2 q(3)^2   360 = q(1)^6 q(2)^3 q(3) Then a(n) is the number of factors of multiplicity one in the q-factorization of n. Also the number of rooted trees appearing only once in the multiset of terminal subtrees of the rooted tree with Matula-Goebel number n. LINKS MATHEMATICA difac[n_]:=If[n==1, {}, With[{i=PrimePi[FactorInteger[n][[1, 1]]]}, Sort[Prepend[difac[n*i/Prime[i]], i]]]]; Table[Count[Length/@Split[difac[n]], 1], {n, 100}] CROSSREFS Cf. A001694, A055231, A056169, A056239, A112798, A118914, A124010. Matula-Goebel numbers: A007097, A061775, A109129, A196050, A317713, A324968. q-factorization: A324922, A324923, A324924, A325614, A325661. Sequence in context: A209599 A238347 A170942 * A342657 A002187 A124756 Adjacent sequences:  A325657 A325658 A325659 * A325661 A325662 A325663 KEYWORD nonn AUTHOR Gus Wiseman, May 13 2019 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 April 10 11:34 EDT 2021. Contains 342845 sequences. (Running on oeis4.)