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

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, 4, 420, 30, 30, 30, 20160, 24, 9240, 420, 12, 30, 60060, 30, 420, 30, 240, 30, 420, 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

Offset: 1

Author

Antti Karttunen, Nov 18 2016

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..550

Crossrefs

Cf. A046523, A051258.

Programs

Mathematica

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 *)
Table[Times @@ MapIndexed[(Prime@ First@ #2)^#1 &, #] &@ If[Length@ # == 1 && #[[1, 1]] == 1, {0}, Reverse@ Sort@ #[[All, -1]]] &@ FactorInteger[
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 *)

PARI

A051258(n) = my(P=polcyclo(n)); sum(i=1, poldegree(P), polcoeff(P, i)*fibonacci(i)); \\ From Charles R Greathouse IV, Jan 05 2013
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
A278158(n) = if(6==n,0,A046523(A051258(n)));
for(n=1, 550, write("b278158.txt", n, " ", A278158(n)));

Scheme

(define (A278158 n) (let ((k (A051258 n))) (if (zero? k) k (A046523 k))))

Formula

a(n) = A046523(A051258(n)), except for n=6, a(6) = 0.