A379483 - OEIS

%I #10 Dec 27 2024 18:25:32

%S 1,1,5,1,1,2,1,1,1,1,3,3,2,1,3,1,1,1,1,1,2,2,3,2,1,3,2,1,1,2,7,1,1,1,

%T 1,1,2,1,1,1,1,5,1,7,1,2,4,4,1,1,2,2,1,4,6,1,3,1,3,4,1,2,1,1,2,1,1,1,

%U 1,1,2,1,1,7,4,1,2,1,1,1,1,1,2,2,1,1,6,2,2,1,7,4,1,2,1,2,6,1,2,1,1,3,1,6,2

%N a(n) is the number of trailing 1-bits in the binary representation of sigma(A003961(n^2)), where A003961 is fully multiplicative with a(prime(i)) = prime(i+1), and sigma is the sum of divisors function.

%H Antti Karttunen, <a href="/A379483/b379483.txt">Table of n, a(n) for n = 1..20000</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>.

%H <a href="/index/Pri#prime_indices">Index entries for sequences related to prime indices in the factorization of n</a>.

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.

%F a(n) = A007814(1+A379482(n)).

%F a(n) = A379222(A048673(n)).

%t {1}~Join~Array[Length@ Last@ Split[IntegerDigits[#, 2]][[1 ;; -1 ;; 2]] &[

%t DivisorSigma[1,

%t   Apply[Times, Map[NextPrime[#1]^#2 & @@ # &, FactorInteger[#]] ]^2] ] &,

%t     105, 2] (* _Michael De Vlieger_, Dec 27 2024 *)

%o (PARI) A379483(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1); f[i, 2] *= 2); valuation(1+sigma(factorback(f)),2); };

%Y Cf. A003961, A003973, A007814, A048673, A379222, A379482, A379483.

%Y Cf. also A336700.

%K nonn

%O 1,3

%A _Antti Karttunen_, Dec 27 2024