cp's OEIS Frontend

A309530 Number of power-of-two-divisors of sum of divisors of sum of divisors of powers of two: a(n) = A001511(A051027(A000079(n))).

%I A309530 #69 Dec 23 2024 14:53:45
%S A309530 1,3,4,4,6,4,8,5,5,10,5,6,14,12,12,6,18,10,20,11,9,9,6,8,8,18,6,15,7,
%T A309530 16,32,7,11,22,17,14,7,24,22,13,5,13,11,12,20,10,7,11,9,16,33,22,6,10,
%U A309530 15,17,28,12,6,20,62,36,12,9,24,16,5,26,12,26,10,18,6,12,16,28,19,26
%N A309530 Number of power-of-two-divisors of sum of divisors of sum of divisors of powers of two: a(n) = A001511(A051027(A000079(n))).
%H A309530 Juri-Stepan Gerasimov, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2019-August/018893.html">x = A001511(A051027(A000079(x)))</a>, SeqFan list, Aug 19 2019.
%F A309530 a(n) = A001511(A051027(A000079(n))).
%e A309530 a(0) = A001511(A051027(A000079(0))) = A001511(A051027(A000079(2^0))) = A001511(A051027(1)) = A001511(1) = 1.
%o A309530 (Magma) [Valuation(2*SumOfDivisors(SumOfDivisors(2^n)),2): n in [0..89]];
%o A309530 (PARI) a(n) = valuation(2*sigma(sigma(2^n)), 2); \\ _Michel Marcus_, Aug 06 2019
%o A309530 (Python)
%o A309530 from sympy import divisor_sigma
%o A309530 def A309530(n): return ((m:=int(divisor_sigma((1<<n+1)-1)))&-m).bit_length() # _Chai Wah Wu_, Jul 13 2022
%Y A309530 Cf. A000043 (numbers m such that m - 1 divides a(m - 1) - 2), A000079, A001511, A051027, A090748.
%K A309530 nonn
%O A309530 0,2
%A A309530 _Juri-Stepan Gerasimov_, Aug 06 2019