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Multiplicative with a(p^e) = phi(sigma(p^e)).
8

%I #9 May 08 2022 15:39:00

%S 1,2,2,6,2,4,4,8,12,4,4,12,6,8,4,30,6,24,8,12,8,8,8,16,30,12,16,24,8,

%T 8,16,36,8,12,8,72,18,16,12,16,12,16,20,24,24,16,16,60,36,60,12,36,18,

%U 32,8,32,16,16,16,24,30,32,48,126,12,16,32,36,16,16,24,96,36,36,60,48,16,24,32,60,110,24,24,48,12

%N Multiplicative with a(p^e) = phi(sigma(p^e)).

%H Antti Karttunen, <a href="/A353752/b353752.txt">Table of n, a(n) for n = 1..16384</a>

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

%F Multiplicative with a(p^e) = A062401(p^e).

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

%F a(n) = A062401(n) - A353753(n).

%o (PARI)

%o A062401(n) = eulerphi(sigma(n));

%o A353752(n) = { my(f = factor(n)); prod(k=1, #f~, A062401(f[k, 1]^f[k, 2])); };

%Y Cf. A000010, A000203, A062401, A353753, A353754, A353755.

%Y Cf. A336547 (positions where equal to A062401), A336548 (positions where less).

%Y Cf. also A353802.

%K nonn,mult

%O 1,2

%A _Antti Karttunen_, May 08 2022