A354198 a(n) = A064989(A064989(sigma(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, 3, 1, 3, 3, 3, 2, 26, 23, 3, 3, 3, 1, 3, 21, 6, 3, 9, 14, 22, 2, 2, 7, 182, 3, 14, 313, 201, 3, 3, 3, 603, 3, 3, 3, 115, 3, 3, 2, 3, 3, 21, 2, 9, 9, 3, 2, 75, 2, 22, 3, 109, 3, 21, 46, 109, 2, 23, 7, 154, 3, 6, 22, 222, 2, 14, 2, 22, 29, 6, 1, 78, 3, 161, 69, 1407, 6, 2, 21, 44, 7, 21, 14, 201, 21, 39, 3, 529

Offset

1,2

Comments

For any hypothetical odd perfect number opn that is not a multiple of 3, it holds that a(n) = A354196(n) = A348750(n) = n, where n = A064989(A064989(opn)). See also comments in A353365.

Links

Table of n, a(n) for n=1..88.

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Formula

a(n) = A064989(A354197(A003961(n))) = A064989(A064989(A066971(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); };
A354198(n) = A064989(A064989(sigma(sigma(sigma(A003961(A003961(n)))))));

Crossrefs

Cf. A000203, A003961, A064989, A066971, A326042, A353365, A354197.

Cf. also A348750, A354196.

Sequence in context: A152774 A275820 A210146 * A233654 A068074 A063195

Adjacent sequences: A354195 A354196 A354197 * A354199 A354200 A354201

Keyword

nonn

Author

Antti Karttunen, May 24 2022

Status

approved