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A354195 a(n) = A064989(sigma(sigma(A003961(n)))), where A003961 shifts the prime factorization one step towards larger primes, and A064989 shifts it back towards smaller primes. 4
1, 5, 2, 5, 6, 6, 5, 12, 1, 20, 2, 10, 22, 29, 29, 85, 10, 5, 6, 30, 66, 6, 4, 58, 3, 66, 25, 25, 20, 113, 6, 25, 5, 58, 20, 5, 2, 20, 15, 226, 10, 220, 29, 10, 6, 12, 6, 170, 3, 15, 12, 110, 10, 145, 29, 40, 319, 78, 2, 145, 20, 18, 5, 541, 319, 29, 66, 50, 110, 78, 34, 12, 58, 6, 66, 30, 6, 87, 5, 510, 8, 58, 44 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
For any hypothetical odd perfect number opn that is not a multiple of 3, it holds that a(n) = A354197(n) = 2*n, where n = A064989(opn) is an odd number.
LINKS
FORMULA
a(n) = A064989(A051027(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); };
A354195(n) = A064989(sigma(sigma(A003961(n))));
CROSSREFS
Cf. A000203, A003961, A051027, A064989, A354196 [= A064989(a(A003961(n)))], A354346 [= 2*n - a(n)].
Cf. also A326042, A354197, A354199.
Sequence in context: A116558 A196626 A082571 * A087300 A074455 A339161
KEYWORD
nonn
AUTHOR
Antti Karttunen, May 23 2022
STATUS
approved

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Last modified June 20 01:56 EDT 2024. Contains 373510 sequences. (Running on oeis4.)