A353416 a(n) = A000593(A252463(n)), where A000593 is the sum of odd divisors, and A252463 is the hybrid shift.

1, 1, 1, 1, 4, 4, 6, 1, 1, 6, 8, 4, 12, 8, 4, 1, 14, 13, 18, 6, 6, 12, 20, 4, 13, 14, 1, 8, 24, 24, 30, 1, 8, 18, 24, 13, 32, 20, 12, 6, 38, 32, 42, 12, 4, 24, 44, 4, 31, 31, 14, 14, 48, 40, 32, 8, 18, 30, 54, 24, 60, 32, 6, 1, 48, 48, 62, 18, 20, 48, 68, 13, 72, 38, 13, 20, 48, 56, 74, 6, 1, 42, 80, 32, 56, 44, 24

Offset: 1

Author

Antti Karttunen, Apr 20 2022

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A000265, A000593 (even bisection), A064989, A252463, A353412.

Cf. also A320107, A353417.

Programs

PARI

A000265(n) = (n>>valuation(n,2));
A000593(n) = sigma(A000265(n));
A064989(n) = { my(f=factor(A000265(n))); for(i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f); };
A252463(n) = if(!(n%2),n/2,A064989(n));
A353416(n) = A000593(A252463(n));

Formula

a(n) = A000593(A252463(n)) = A000203(A353412(n)).

a(2*n) = A000593(n).

a(n) <= A000593(n) for all n >= 1.