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

1,3

Links

Table of n, a(n) for n=1..90.

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Formula

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

Prog

(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))))));

Crossrefs

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

Cf. also A348750.

Sequence in context: A337894 A337892 A337891 * A059333 A345761 A106485

Adjacent sequences: A354193 A354194 A354195 * A354197 A354198 A354199

Keyword

nonn

Author

Antti Karttunen, May 23 2022

Status

approved