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The 3-adic valuation of 1+A000265(sigma(n)), where A000265 gives the odd part.
4

%I #15 Feb 22 2021 21:20:03

%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,

%T 0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,2,0,

%U 0,0,0,0,0,0,0,2,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0

%N The 3-adic valuation of 1+A000265(sigma(n)), where A000265 gives the odd part.

%H Antti Karttunen, <a href="/A337196/b337196.txt">Table of n, a(n) for n = 1..65537</a>

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

%F a(n) = A007949(A337194(n)) = A007949(1+A000265(A000203(n))).

%F a(n) = A007949(A336698(n)).

%t Array[IntegerExponent[1 + #/2^IntegerExponent[#, 2], 3] &@ DivisorSigma[1, #] &, 105] (* _Michael De Vlieger_, Feb 22 2021 *)

%o (PARI)

%o A007949(n) = valuation(n,3);

%o A000265(n) = (n>>valuation(n,2));

%o A337196(n) = A007949(1+A000265(sigma(n)));

%Y Cf. A000203, A000265, A007949, A074941, A161942, A336698, A336700, A337194, A337195.

%Y Cf. A337197 (the first occurrence of each n).

%K nonn

%O 1,67

%A _Antti Karttunen_, Aug 18 2020