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

1,5

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)

Formula

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

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

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

Prog

(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));

Crossrefs

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

Cf. also A320107, A353417.

Sequence in context: A142154 A084458 A248933 * A110356 A200348 A205868

Adjacent sequences: A353413 A353414 A353415 * A353417 A353418 A353419

Keyword

nonn

Author

Antti Karttunen, Apr 20 2022

Status

approved