A354197 a(n) = A064989(sigma(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, 5, 2, 2, 10, 5, 44, 20, 11, 6, 6, 5, 5, 5, 3, 2, 20, 10, 4, 10, 12, 66, 6, 58, 10, 204, 204, 11, 5, 10, 986, 20, 2, 55, 113, 20, 55, 12, 2, 5, 55, 5, 29, 40, 132, 12, 15, 40, 58, 132, 10, 6, 6, 6, 18, 5, 8, 20, 6, 22, 145, 78, 262, 5, 20, 10, 170, 10, 40, 6, 2486, 2, 40, 50, 12, 40, 12, 20, 6, 60, 5, 110, 20

Offset

1,3

Comments

For any hypothetical odd perfect number opn that is not a multiple of 3, it holds that a(n) = A354195(n) = 2*n, where n = A064989(opn).

Links

Table of n, a(n) for n=1..84.

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Formula

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

Crossrefs

Cf. A000203, A003961, A064989, A066971, A354198 [= A064989(a(A003961(n)))].

Cf. also A326042, A354195.

Sequence in context: A201328 A199189 A145438 * A346040 A244290 A175232

Adjacent sequences: A354194 A354195 A354196 * A354198 A354199 A354200

Keyword

nonn

Author

Antti Karttunen, May 24 2022

Status

approved