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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.
2
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.
FORMULA
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, May 24 2022
STATUS
approved