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a(n) = A064989(A064989(sigma(sigma(A003961(A003961(n)))))), where A003961 shifts the prime factorization of n one step towards larger primes, and A064989 shifts it back towards smaller primes.
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%I #6 May 23 2022 17:45:32

%S 1,1,2,1,3,23,1,9,2,14,7,2,3,3,3,1,2,14,1,3,23,6,3,9,2,2,529,1,2,763,

%T 1,7,161,161,2,2,3,21,3,483,23,3,2,7,42,109,3,2,23,2,109,3,1,69,4,6,

%U 23,6,3,3,14,21,2,3133,23,6,13,2,201,161,23,126,3,2,4,1,21,109,7,3,461,21,13,23,21,75,46,12,1,8

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

%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(A354195(A003961(n))) = A064989(A064989(A051027(A003961(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 A354196(n) = A064989(A064989(sigma(sigma(A003961(A003961(n))))));

%Y Cf. A000203, A003961, A051027, A064989, A354195.

%Y Cf. also A348750.

%K nonn

%O 1,3

%A _Antti Karttunen_, May 23 2022