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a(n) = 2*n - A064989(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 #12 May 26 2022 20:43:41

%S 1,-1,4,3,4,6,9,4,17,0,20,14,4,-1,1,-53,24,31,32,10,-24,38,42,-10,47,

%T -14,29,31,38,-53,56,39,61,10,50,67,72,56,63,-146,72,-136,57,78,84,80,

%U 88,-74,95,85,90,-6,96,-37,81,72,-205,38,116,-25,102,106,121,-413,-189,103,68,86,28,62,108,132,88,142,84

%N a(n) = 2*n - A064989(sigma(sigma(A003961(n)))), where A003961 shifts the prime factorization one step towards larger primes, and A064989 shifts it back towards smaller primes.

%C No other zeros <= 2^25 than a(10) and a(105270).

%H Antti Karttunen, <a href="/A354346/b354346.txt">Table of n, a(n) for n = 1..20000</a>

%H Antti Karttunen, <a href="/A354346/a354346.txt">Data supplement: n, a(n) computed for n = 1..105270</a>

%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) = 2*n - A354195(n) = 2*n - A064989(sigma(sigma(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 A354195(n) = A064989(sigma(sigma(A003961(n))));

%o A354346(n) = (n+n - A354195(n));

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

%Y Cf. also A033879.

%K sign

%O 1,3

%A _Antti Karttunen_, May 25 2022