A354346 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.

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

Offset: 1

Author

Antti Karttunen, May 25 2022

Keywords

• sign

Comments

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

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..105270
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A003961, A064989, A354195.

Cf. also A033879.

Programs

PARI

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A064989(n) = { my(f=factor(n>>valuation(n, 2))); for(i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f); };
A354195(n) = A064989(sigma(sigma(A003961(n))));
A354346(n) = (n+n - A354195(n));

Formula

a(n) = 2*n - A354195(n) = 2*n - A064989(sigma(sigma(A003961(n)))).