A307314 Number of divisors d of 2n such that adding d to 2n in binary requires no carries.

1, 2, 1, 3, 2, 3, 1, 4, 2, 3, 1, 5, 1, 2, 1, 5, 2, 5, 1, 5, 2, 2, 1, 7, 2, 2, 2, 4, 1, 3, 1, 6, 2, 4, 1, 7, 2, 3, 1, 7, 2, 4, 1, 3, 2, 2, 1, 9, 1, 4, 2, 3, 1, 4, 1, 6, 1, 2, 1, 6, 1, 2, 1, 7, 4, 6, 1, 6, 2, 3, 1, 10, 2, 3, 1, 4, 1, 3, 1, 9

Offset

1,2

Comments

Equivalently, number of numbers d such that d|2n and d AND 2n = 0.

First differences of either bisection of A325123.

A001511(n) <= a(n) <= A000005(n).

Links

Table of n, a(n) for n=1..80.

Formula

a(p) = 1 + [p is in A247068] for p prime, where [] is the Iverson bracket.

Prog

(PARI) a(n) = sumdiv(2*n, d, bitand(d, 2*n) == 0); \\ Michel Marcus, Apr 02 2019

Crossrefs

Cf. A325123, A001511, A000005, A247068.

Sequence in context: A159918 A278573 A108663 * A057940 A097285 A057432

Adjacent sequences: A307311 A307312 A307313 * A307315 A307316 A307317

Keyword

nonn

Author

Charlie Neder, Apr 02 2019

Status

approved