This site is supported by donations to The OEIS Foundation.

 Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A124859 Multiplicative with p^e -> primorial(e), p prime and e > 0. 9
 1, 2, 2, 6, 2, 4, 2, 30, 6, 4, 2, 12, 2, 4, 4, 210, 2, 12, 2, 12, 4, 4, 2, 60, 6, 4, 30, 12, 2, 8, 2, 2310, 4, 4, 4, 36, 2, 4, 4, 60, 2, 8, 2, 12, 12, 4, 2, 420, 6, 12, 4, 12, 2, 60, 4, 60, 4, 4, 2, 24, 2, 4, 12, 30030, 4, 8, 2, 12, 4, 8, 2, 180, 2, 4, 12, 12, 4, 8, 2, 420, 210, 4, 2, 24, 4, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Indranil Ghosh, Table of n, a(n) for n = 1..5000 (first 1000 terms from R. Zumkeller) Eric Weisstein's World of Mathematics, Prime Factorization Eric Weisstein's World of Mathematics, Primorial FORMULA a(A000040(x)^n) = A002110(n); a(A002110(n)) = A000079(n); a(A005117(n)) = 2^A001221(A005117(n)) = A072048(n); A001221(a(n)) = A051903(n); A001222(a(n)) = A001222(n). From Antti Karttunen, Mar 06 2017: (Start) a(1) = 1, for n > 1, a(n) = A002110(A067029(n)) * a(A028234(n)). a(n) = A278159(A156552(n)). a(A278159(n)) = A278222(n). a(a(n)) = A046523(n). [after Matthew Vandermast's May 19 2012 formula for the latter sequence] A181819(a(n)) = A238745(n). [after Matthew Vandermast's formula for the latter sequence] (End) EXAMPLE From Michael De Vlieger, Mar 06 2017: (Start) a(2) = 2 since 2 = 2^1, thus primorial p_1# = 2. a(4) = 6 since 4 = 2^2, thus primorial p_2# = 2*3 = 6. a(6) = 4 because 6 is squarefree with omega(6)=2, thus 2^2 = 4. a(8) = 30 since 8 = 2^3, thus primorial p_3# = 2*3*5 = 30. a(10) = 4 since 10 is squarefree with omega(10)=2, thus 2^2 = 4. a(12) = 12 since 12 = 2^1 * 3^2, thus primorials p_1# * p_2# = 2*6 = 12. (End) MAPLE A124859 := proc(n)     local a, pf;     a := 1;     for pf in ifactors(n)[2] do         a := a*A002110(pf[2]) ;     end do:     a ; end proc: seq(A124859(n), n=1..80) ; # R. J. Mathar, Oct 06 2017 MATHEMATICA Table[Which[n == 1, 1, SquareFreeQ@ n, 2^PrimeNu@ n, True, Times @@ Map[Times @@ Prime@ Range@ # &, #[[All, -1]]]] &@ FactorInteger@ n, {n, 86}] (* Michael De Vlieger, Mar 06 2017 *) PROG (PARI) a(n) = {my(f = factor(n)); for (k=1, #f~, f[k, 1] = prod(j=1, f[k, 2], prime(j)); f[k, 2] = 1; ); factorback(f); } \\ Michel Marcus, Nov 16 2015 (Scheme) (define (A124859 n) (cond ((= 1 n) 1) (else (* (A002110 (A067029 n)) (A124859 (A028234 n)))))) ;; Antti Karttunen, Mar 06 2017 (Python) from sympy.ntheory.factor_ import core from sympy import factorint, primorial, primefactors from operator import mul def omega(n): return 0 if n==1 else len(primefactors(n)) def a(n):     f=factorint(n)     return n if n<3 else 2**omega(n) if core(n) == n else reduce(mul, [primorial(f[i]) for i in f]) # Indranil Ghosh, May 13 2017 CROSSREFS Cf. A000040, A000079, A001221, A001222, A002110, A005117, A028234, A046523, A067029, A072048, A108951, A156552, A181819, A238745, A278159, A278222. Sequence in context: A253139 A318519 A317848 * A021446 A062401 A286383 Adjacent sequences:  A124856 A124857 A124858 * A124860 A124861 A124862 KEYWORD nonn,mult AUTHOR Reinhard Zumkeller, Nov 10 2006 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 December 13 08:08 EST 2018. Contains 318082 sequences. (Running on oeis4.)