A351442 - OEIS

%I #14 Feb 12 2022 23:47:39

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

%T 24,2,8,2,72,18,8,6,16,12,2,10,12,24,4,2,30,36,60,4,36,8,8,4,8,4,16,8,

%U 12,30,2,12,126,12,4,16,24,2,4,4,96,36,36,30,24,2,12,4,60,100,24,12,6,8,20,8

%N a(n) = A003958(sigma(n)), where A003958 is multiplicative with a(p^e) = (p-1)^e and sigma is the sum of divisors function.

%C Question: Are there more fixed points than 1, 2, 8, 128, 288, 720, 32768, 29719872, ..., 2147483648 ?

%H Antti Karttunen, <a href="/A351442/b351442.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 Multiplicative with a(p^e) = A003958(1 + p + ... + p^e).

%F a(n) = A003958(A000203(n)).

%F a(n) = A351444(n) - A322582(n) = A351445(n) + A003958(n).

%o (PARI)

%o A003958(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]--); factorback(f); };

%o A351442(n) = A003958(sigma(n));

%Y Cf. A000203, A003958, A322582, A339905, A351443, A351444, A351445, A351446, A351447, A351448, A351456.

%Y Cf. also A348512.

%K nonn,mult

%O 1,2

%A _Antti Karttunen_, Feb 12 2022