%I #10 Nov 15 2024 15:12:11

%S 1,4,7,8,12,28,15,24,14,39,28,56,24,60,60,32,39,56,42,96,63,91,60,168,

%T 32,96,90,120,72,195,63,104,124,120,124,112,60,168,120,234,96,252,84,

%U 224,168,195,124,224,80,128,195,192,120,360,195,360,186,234,168,480,96,252,210,128,224,403,126,312,252,403,195

%N a(n) = sigma(sigma(A350388(n))) * sigma(sigma(A350389(n))), where A350388 and A350389 are the largest unitary divisor of n that is a square, and the largest unitary divisor of n that is an exponentially odd number, respectively.

%C Differs from A051027 at 52, 98, 156, 164, 245, ..., = A377991.

%H Antti Karttunen, <a href="/A377990/b377990.txt">Table of n, a(n) for n = 1..20000</a>

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

%F a(n) = A051027(A350388(n)) * A051027(A350389(n)).

%F a(n) = sigma(A351568(n)) * sigma(A351569(n)).

%o (PARI)

%o A350388(n) = { my(m=1, f=factor(n)); for(k=1,#f~,if(0==(f[k,2]%2), m *= (f[k,1]^f[k,2]))); (m); };

%o A350389(n) = { my(m=1, f=factor(n)); for(k=1,#f~,if(1==(f[k,2]%2), m *= (f[k,1]^f[k,2]))); (m); };

%o A377990(n) = (sigma(sigma(A350388(n))) * sigma(sigma(A350389(n))));

%Y Cf. A000203, A051027, A350388, A350389, A351568, A351569, A377991.

%K nonn,new

%O 1,2

%A _Antti Karttunen_, Nov 15 2024