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A364557 Möbius transform of A005941.

%I A364557 #14 Jul 29 2023 15:59:07
%S A364557 1,1,2,2,4,2,8,4,4,4,16,4,32,8,4,8,64,4,128,8,8,16,256,8,8,32,8,16,
%T A364557 512,4,1024,16,16,64,8,8,2048,128,32,16,4096,8,8192,32,8,256,16384,16,
%U A364557 16,8,64,64,32768,8,16,32,128,512,65536,8,131072,1024,16,32,32,16,262144,128,256,8,524288,16,1048576,2048
%N A364557 Möbius transform of A005941.
%H A364557 Antti Karttunen, <a href="/A364557/b364557.txt">Table of n, a(n) for n = 1..10000</a>
%F A364557 a(n) = Sum_{d|n} A008683(n/d) * A005941(d).
%F A364557 a(1) = 1; for n > 1, a(n) = A297112(n) = 2^(A297113(n)-1) = 2^A297167(n).
%o A364557 (PARI) A364557(n) = if(1==n, 1, 2^(primepi(vecmax(factor(n)[, 1]))+(bigomega(n)-omega(n))-1));
%o A364557 (PARI)
%o A364557 A005941(n) = { my(f=factor(n), p, p2=1, res=0); for(i=1, #f~, p = 1 << (primepi(f[i, 1])-1); res += (p * p2 * (2^(f[i, 2])-1)); p2 <<= f[i, 2]); (1+res) }; \\ (After _David A. Corneth_'s program for A156552)
%o A364557 A364557(n) = sumdiv(n,d,moebius(n/d)*A005941(d));
%o A364557 (Python)
%o A364557 from sympy import factorint, primepi
%o A364557 def A364557(n): return 1<<primepi(max(f:=factorint(n)))+sum(e-1 for e in f.values())-1 if n>1 else 1 # _Chai Wah Wu_, Jul 29 2023
%Y A364557 Cf. A005941, A008683, A297112, A297113, A297167, A364558.
%K A364557 nonn
%O A364557 1,3
%A A364557 _Antti Karttunen_, Jul 28 2023