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a(n) = A064989(sigma(sigma(sigma(A003961(n))))), where A003961 shifts the prime factorization one step towards larger primes, and A064989 shifts it back towards smaller primes.
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%I #8 May 24 2022 16:31:42

%S 1,1,5,2,2,10,5,44,20,11,6,6,5,5,5,3,2,20,10,4,10,12,66,6,58,10,204,

%T 204,11,5,10,986,20,2,55,113,20,55,12,2,5,55,5,29,40,132,12,15,40,58,

%U 132,10,6,6,6,18,5,8,20,6,22,145,78,262,5,20,10,170,10,40,6,2486,2,40,50,12,40,12,20,6,60,5,110,20

%N a(n) = A064989(sigma(sigma(sigma(A003961(n))))), where A003961 shifts the prime factorization one step towards larger primes, and A064989 shifts it back towards smaller primes.

%C For any hypothetical odd perfect number opn that is not a multiple of 3, it holds that a(n) = A354195(n) = 2*n, where n = A064989(opn).

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

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

%F a(n) = A064989(A066971(A003961(n))).

%o (PARI)

%o A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };

%o A064989(n) = { my(f=factor(n>>valuation(n, 2))); for(i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f); };

%o A354197(n) = A064989(sigma(sigma(sigma(A003961(n)))));

%Y Cf. A000203, A003961, A064989, A066971, A354198 [= A064989(a(A003961(n)))].

%Y Cf. also A326042, A354195.

%K nonn

%O 1,3

%A _Antti Karttunen_, May 24 2022