cp's OEIS Frontend

A286357 One more than the exponent of the highest power of 2 dividing sigma(n): a(n) = A001511(A000203(n)).

%I A286357 #20 Sep 04 2023 19:30:33
%S A286357 1,1,3,1,2,3,4,1,1,2,3,3,2,4,4,1,2,1,3,2,6,3,4,3,1,2,4,4,2,4,6,1,5,2,
%T A286357 5,1,2,3,4,2,2,6,3,3,2,4,5,3,1,1,4,2,2,4,4,4,5,2,3,4,2,6,4,1,3,5,3,2,
%U A286357 6,5,4,1,2,2,3,3,6,4,5,2,1,2,3,6,3,3,4,3,2,2,5,4,8,5,4,3,2,1,3,1,2,4,4,2,7,2,3,4,2,4,4,4,2,5,5,2,2,3,5,4
%N A286357 One more than the exponent of the highest power of 2 dividing sigma(n): a(n) = A001511(A000203(n)).
%H A286357 Antti Karttunen, <a href="/A286357/b286357.txt">Table of n, a(n) for n = 1..10000</a>
%H A286357 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A286357 a(n) = A001511(A000203(n)).
%F A286357 a(n) = 1 + A000523(A000203(n)/A161942(n)). [See also A082903.]
%F A286357 a(n) = 1 iff A053866(n) = 1.
%t A286357 Table[IntegerExponent[DivisorSigma[1,n],2]+1,{n,120}] (* _Harvey P. Dale_, Sep 04 2023 *)
%o A286357 (PARI)
%o A286357 A001511(n) = (1+valuation(n,2));
%o A286357 A286357(n) = A001511(sigma(n));
%o A286357 for(n=1, 10000, write("b286357.txt", n, " ", A286357(n)));
%o A286357 (Scheme)
%o A286357 (define (A286357 n) (A001511 (A000203 n)))
%o A286357 (define (A286357 n) (A070939 (/ (A000203 n) (A161942 n))))
%o A286357 (Python)
%o A286357 from sympy import divisor_sigma as D
%o A286357 def a001511(n): return bin(n)[2:][::-1].index("1") + 1
%o A286357 def a(n): return a001511(D(n)) # _Indranil Ghosh_, May 12 2017
%o A286357 (Python)
%o A286357 from sympy import divisor_sigma
%o A286357 def A286357(n): return ((m:=int(divisor_sigma(n)))&-m).bit_length() # _Chai Wah Wu_, Jul 10 2022
%Y A286357 Cf. A000203, A000523, A001511, A053866, A070939, A082903, A161942, A286358.
%K A286357 nonn
%O A286357 1,3
%A A286357 _Antti Karttunen_, May 10 2017