A353803 - OEIS

%I #8 May 15 2022 12:34:14

%S 0,0,0,0,0,0,0,0,0,9,0,0,0,0,24,0,0,0,0,0,42,21,0,0,0,0,0,0,0,141,0,0,

%T 72,36,56,0,0,0,48,54,0,168,0,0,0,45,0,0,0,0,78,21,0,0,141,0,108,54,0,

%U 192,0,0,0,0,64,381,0,0,168,317,0,0,0,0,0,0,168,192,0,0,0,72,0,336,188,0,144,126,0,126,112

%N a(n) = Product_{p^e||n} sigma(sigma(p^e)) - sigma(sigma(n)), where n = Product_{p^e||n}, with each p^e the maximal power of prime p that divides n.

%H Antti Karttunen, <a href="/A353803/b353803.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) = A353802(n) - A051027(n).

%o (PARI)

%o A051027(n) = sigma(sigma(n));

%o A353803(n) = { my(f = factor(n)); (prod(k=1, #f~, A051027(f[k, 1]^f[k, 2])) - A051027(n)); };

%Y Cf. A000203, A051027, A353802, A353804, A353805, A353806.

%Y Cf. A336547 (positions of 0's), A336548 (positions of terms > 0).

%Y Cf. also A353753.

%K nonn

%O 1,10

%A _Antti Karttunen_, May 08 2022