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.

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

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

Antti Karttunen, Table of n, a(n) for n = 1..20000

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

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

Adjacent sequences: A354192 A354193 A354194 * A354196 A354197 A354198

Keyword

nonn

Author

Antti Karttunen, May 23 2022

Status

approved