cp's OEIS Frontend

A278158 Least number with the prime signature of the n-th Fibocyclotomic number, with a(6) = 0.

%I A278158 #19 Nov 22 2016 21:47:19
%S A278158 1,1,2,1,2,0,12,2,6,1,6,2,24,4,2,6,60,6,60,6,6,6,6,12,6,24,210,24,30,
%T A278158 4,420,30,30,30,20160,24,9240,420,12,30,60060,30,420,30,240,30,420,
%U A278158 210,27720,30,60,720,420,420,6,720,2310,30,210,30,2042040,4620,24,210,7680,60,60060,210,6,30240,510510,2160,6486480,840,2310,9240,9240,420,60060,210
%N A278158 Least number with the prime signature of the n-th Fibocyclotomic number, with a(6) = 0.
%H A278158 Antti Karttunen, <a href="/A278158/b278158.txt">Table of n, a(n) for n = 1..550</a>
%F A278158 a(n) = A046523(A051258(n)), except for n=6, a(6) = 0.
%t A278158 ps[n_] := Sort[Last /@ FactorInteger[n]]; g[n_] := Module[{cy = CoefficientList[ Cyclotomic[n, x], x]}, Total[Times @@@ Thread[{Fibonacci[Range[0, Length[cy] - 1]], cy}]]]; f[n_] := Block[{c = ps[g[n]]}, lng = Length@ c; Times @@ (Reverse[ Prime[ Range[ lng]]]^c)]; f[6] = 0; f[1] = f[2] = f[4] = f[10] = 1; Array[f, 70] (* _Robert G. Wilson v_, Nov 19 2016 *)
%t A278158 Table[Times @@ MapIndexed[(Prime@ First@ #2)^#1 &, #] &@ If[Length@ # == 1 && #[[1, 1]] == 1, {0}, Reverse@ Sort@ #[[All, -1]]] &@ FactorInteger[
%t A278158 Total[Times @@@ Thread[{Fibonacci[Range[0, Length@ # - 1]], #}]] &@ CoefficientList[Cyclotomic[n, x], x] + Boole[n == 0]], {n, 120}] (* _Michael De Vlieger_, Nov 21 2016, after _Harvey P. Dale_ at A051258 *)
%o A278158 (PARI)
%o A278158 A051258(n) = my(P=polcyclo(n)); sum(i=1, poldegree(P), polcoeff(P, i)*fibonacci(i)); \\ From _Charles R Greathouse IV_, Jan 05 2013
%o A278158 A046523(n) = my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]) \\ From _Charles R Greathouse IV_, Aug 17 2011
%o A278158 A278158(n) = if(6==n,0,A046523(A051258(n)));
%o A278158 for(n=1, 550, write("b278158.txt", n, " ", A278158(n)));
%o A278158 (Scheme) (define (A278158 n) (let ((k (A051258 n))) (if (zero? k) k (A046523 k))))
%Y A278158 Cf. A046523, A051258.
%K A278158 nonn
%O A278158 1,3
%A A278158 _Antti Karttunen_, Nov 18 2016