A354196 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.

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, 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, 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

Offset: 1

Author

Antti Karttunen, May 23 2022

Keywords

• nonn

Links

• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

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

Cf. also A348750.

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); };
A354196(n) = A064989(A064989(sigma(sigma(A003961(A003961(n))))));

Formula

a(n) = A064989(A354195(A003961(n))) = A064989(A064989(A051027(A003961(A003961(n))))).