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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.
3
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).
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. also A326042, A354195.
Sequence in context: A201328 A199189 A145438 * A346040 A244290 A175232
KEYWORD
nonn
AUTHOR
Antti Karttunen, May 24 2022
STATUS
approved