This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A077565 Number of factorizations of n where each factor has a different prime signature. 4
 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 3, 1, 3, 1, 1, 1, 4, 1, 1, 2, 3, 1, 4, 1, 3, 1, 1, 1, 3, 1, 1, 1, 4, 1, 4, 1, 3, 3, 1, 1, 6, 1, 3, 1, 3, 1, 4, 1, 4, 1, 1, 1, 5, 1, 1, 3, 4, 1, 4, 1, 3, 1, 4, 1, 7, 1, 1, 3, 3, 1, 4, 1, 6, 2, 1, 1, 5, 1, 1, 1, 4, 1, 5, 1, 3, 1, 1, 1, 9, 1, 3, 3, 3, 1, 4, 1, 4, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 COMMENTS In contrast to A001055 this sequence excludes from the count all such factorizations of n that include two such factors, f and g, for which it would hold that A046523(f) = A046523(g), or equally A101296(f) = A101296(g). - Antti Karttunen, Nov 24 2017 REFERENCES Amarnath Murthy, Generalization of partition function. Introducing Smarandache Factor Partition. Smarandache Notions Journal, Vol. 11, 1-2-3,2000. LINKS David A. Corneth, Table of n, a(n) for n = 1..10000 (first 6143 terms from Antti Karttunen, computed with the given Scheme-program) Antti Karttunen, Scheme-program for computing this sequence FORMULA a(n) <= A001055(n). - Antti Karttunen, Nov 24 2017 a(p^e) = A000009(p^e). - David A. Corneth, Nov 24 2017 EXAMPLE a(24) = 4, 24 = 12*2 = 8*3 = 6*4. The factorizations 2*3*4, 2*2*2*3 etc. are not counted. From Antti Karttunen, Nov 24 2017: (Start) For n = 30 the solutions are 30, 2*15, 3*10, 5*6, thus a(30) = 4. For n = 36 the solutions are 36, 2*18, 3*12, thus a(36) = 3. For n = 60 the solutions are 60, 2*30, 3*20, 4*15, 5*12, thus a(60) = 5. For n = 72 the solutions are 72, 2*36, 3*24, 4*18, 6*12, 8*9, 3*4*6, thus a(72) = 7. (End) MATHEMATICA Table[1 + Count[Subsets[Rest@ Divisors@ n, {2, Infinity}], _?(And[Times @@ # == n, UnsameQ @@ Map[Sort[FactorInteger[#][[All, -1]], Greater] &, #]] &)], {n, 105}] (* Michael De Vlieger, Nov 24 2017 *) CROSSREFS Cf. A000009, A001055, A025487, A077563, A077564, A077566, A046523, A101296. Sequence in context: A224765 A160267 A115621 * A316979 A115561 A115622 Adjacent sequences:  A077562 A077563 A077564 * A077566 A077567 A077568 KEYWORD nonn AUTHOR Amarnath Murthy, Nov 11 2002 EXTENSIONS Corrected and extended by Ray Chandler, Aug 26 2003 Name improved by Antti Karttunen and David A. Corneth, Nov 24 2017 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 March 21 12:04 EDT 2019. Contains 321369 sequences. (Running on oeis4.)