cp's OEIS Frontend

A166120 a(n) = A027642(n-1) / A089026(n).

%I A166120 #11 Aug 20 2022 13:38:29
%S A166120 1,1,2,1,6,1,6,1,30,1,6,1,210,1,6,1,30,1,42,1,330,1,6,1,2730,1,6,1,30,
%T A166120 1,462,1,510,1,6,1,51870,1,6,1,330,1,42,1,690,1,6,1,46410,1,66,1,30,1,
%U A166120 798,1,870,1,6,1,930930,1,6,1,510,1,966,1,30,1,66,1,1919190,1,6,1,30,1,42,1
%N A166120 a(n) = A027642(n-1) / A089026(n).
%C A166120 As in A166062, the offset is rather arbitrary.
%C A166120 The sequence contains numbers like 210 which are not in A006954.
%C A166120 One could also consider dividing by the largest prime divisor of A027642 instead of A089026, which yields 1, 1, 2, 1, 6, 1, 6, 1, 6, 1, 6, 1, 210, 1, 2, 1, 30, 1, 42, 1, 30, ... as an alternative version.
%C A166120 These are the Clausen numbers based on the proper divisors of n whereas the classical Clausen numbers A160014 are based on all divisors of n. (The proper divisors are the divisors of n that are less than n.) - _Peter Luschny_, Aug 20 2022
%p A166120 A027642 := proc(n) denom(bernoulli(n)) ; end:
%p A166120 A089026 := proc(n) if isprime(n) then n; else 1; end if; end proc:
%p A166120 A166120 := proc(n) A027642(n-1)/A089026(n) ; end proc: seq(A166120(n), n=1..80) ; # _R. J. Mathar_, Mar 25 2010
%p A166120 # Second program, assuming offset 0:
%p A166120 clausen := proc(n) if irem(n,2)=1 then 1 else numtheory[divisors](n) minus {n};
%p A166120 map(i -> i+1, %); select(isprime, %); mul(i, i=%) fi end:
%p A166120 seq(clausen(n), n = 0..79); # _Peter Luschny_, Aug 20 2022
%Y A166120 Cf. A027642, A089026, A160014.
%K A166120 nonn
%O A166120 1,3
%A A166120 _Paul Curtz_, Oct 07 2009
%E A166120 Extended by _R. J. Mathar_, Mar 25 2010