A118678 -id:A118678 - cp's OEIS frontend

A154430 Odd squarefree numbers n such that the cyclotomic polynomial Phi(n,x) has height > 1.

105, 165, 195, 255, 273, 285, 345, 357, 385, 429, 455, 555, 561, 595, 609, 615, 627, 645, 665, 705, 715, 759, 777, 795, 805, 897, 935, 957, 969, 987, 1001, 1005, 1015, 1023, 1045, 1065, 1085, 1095, 1105, 1131, 1155, 1185, 1221, 1235, 1239, 1245, 1265

Offset: 1

T. D. Noe, Jan 09 2009

nonn

The height of a polynomial is the maximum of the absolute value of its coefficients. Different from A118678, which excludes terms that are a multiple of smaller terms.

T. D. Noe, Table of n, a(n) for n = 1..1000

Cf. A013590, A117318, A117223, A152940, A152941, A152942, A152943, A152955.

Select[Range[2000], OddQ[#] && SquareFreeQ[#] && Max[ Abs[ CoefficientList[ Cyclotomic[#, x], x]]] > 1&] (* Jean-François Alcover, Nov 14 2016 *)

is(n)=issquarefree(n) && n%2 && vecmax(abs(Vec(polcyclo(n))))>1 \\ Charles R Greathouse IV, Nov 05 2017

A189936 Odd numbers in A076763.

Original entry on oeis.org

105, 165, 195, 255, 273, 315, 345, 357, 385, 399, 465, 483, 525, 555, 585, 627, 663, 693, 705, 735, 765, 777, 795, 897, 915, 957, 975, 1005, 1095, 1113, 1155, 1173, 1185, 1281, 1295, 1305, 1353, 1365, 1515, 1545, 1575, 1617, 1677, 1683, 1725, 1755, 1785, 1815, 1935, 1953

Offset: 1

Juri-Stepan Gerasimov, May 01 2011

nonn

G. C. Greubel, Table of n, a(n) for n = 1..5000

Cf. A001221, A076763, A013590, A118678, A154430.

omega := proc(n) nops( numtheory[factorset](n)) ; end proc:
isA076763 := proc(n) omega(n) > omega(n-1) and omega(n) > omega(n+1) ; end proc:
isA189936 := proc(n) type(n,'odd') and isA076763(n) ; end proc:
for n from 1 to 2000 by 2 do if isA189936(n) then printf("%d,",n) ; end if; end do;  # R. J. Mathar, May 26 2011

Select[Range[1, 2000, 2], PrimeNu[# - 1] < PrimeNu[#] > PrimeNu[# + 1]&] (* Jean-François Alcover, Nov 14 2016 *)
Select[#[[2,1]]&/@Select[Partition[Table[{n,PrimeNu[n]},{n,2000}],3,1], #[[1,2]] <#[[2,2]]>#[[3,2]]&],OddQ] (* Harvey P. Dale, Sep 15 2019 *)

a(n) = A005408(k) = A076763(m).

Corrected by R. J. Mathar, May 26 2011

cp's OEIS Frontend

A154430 Odd squarefree numbers n such that the cyclotomic polynomial Phi(n,x) has height > 1.

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