The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A359079 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A359079

a(n) is the sum of the divisors d of 2*n such that the binary expansions of d and 2*n have no common 1-bit.
(history; published version)

#10 by Michael De Vlieger at Fri Dec 16 11:52:09 EST 2022

STATUS

reviewed

approved

#9 by Hugo Pfoertner at Fri Dec 16 11:20:23 EST 2022

STATUS

proposed

reviewed

#8 by Rémy Sigrist at Fri Dec 16 10:43:16 EST 2022

STATUS

editing

proposed

#7 by Rémy Sigrist at Fri Dec 16 10:42:36 EST 2022

LINKS

Rémy Sigrist, <a href="/A359079/b359079.txt">Table of n, a(n) for n = 1..10000</a>

STATUS

approved

editing

Discussion

Fri Dec 16

10:43

Rémy Sigrist: added b-file

#6 by Michael De Vlieger at Fri Dec 16 09:03:42 EST 2022

STATUS

proposed

approved

#5 by Rémy Sigrist at Fri Dec 16 03:18:25 EST 2022

STATUS

editing

proposed

#4 by Michael S. Branicky at Thu Dec 15 13:47:30 EST 2022

PROG

(Python)

from sympy import divisors as divs

def a(n): return sum(d for d in divs(2*n, generator=True) if (d>>1)&n == 0)

print([a(n) for n in range(1, 75)]) # Michael S. Branicky, Dec 15 2022

#3 by Rémy Sigrist at Thu Dec 15 12:37:45 EST 2022

MATHEMATICA

a[n_] := DivisorSum[2n, #*Boole[BitAnd[#, 2n] == 0] &]; Array[a, 74]

CROSSREFS

Cf. A246601, A346878.

#2 by Rémy Sigrist at Thu Dec 15 12:32:08 EST 2022

NAME

allocated for Rémy Sigrist

a(n) is the sum of the divisors d of 2*n such that the binary expansions of d and 2*n have no common 1-bit.

DATA

1, 3, 1, 7, 6, 6, 1, 15, 10, 13, 1, 16, 1, 3, 1, 31, 18, 33, 1, 32, 22, 3, 1, 36, 6, 3, 10, 14, 1, 6, 1, 63, 34, 54, 1, 70, 38, 22, 1, 70, 42, 48, 1, 7, 6, 3, 1, 76, 1, 38, 18, 7, 1, 24, 1, 36, 1, 3, 1, 21, 1, 3, 1, 127, 84, 116, 1, 126, 70, 38, 1, 153, 74, 77

OFFSET

1,2

COMMENTS

Odd numbers share a 1-bit (2^0) with all their divisors, hence this sequence deals with even numbers.

LINKS

<a href="/index/Di#divisors">Index entries for sequences related to divisors</a>

FORMULA

a(n) <= A346878(n) with equality iff n is a power of 2.

EXAMPLE

For n = 6:

- the divisors of 12 are:

d bin(d) common bit?

-- ------ -----------

1 1 no

2 10 no

3 11 no

4 100 yes

6 110 yes

12 1100 yes

- hence a(6) = 1 + 2 + 3 = 6.

PROG

(PARI) a(n) = sumdiv(2*n, d, if (bitand(2*n, d)==0, d, 0))

CROSSREFS

Cf. A346878.

KEYWORD

allocated

nonn,base

AUTHOR

Rémy Sigrist, Dec 15 2022

STATUS

approved

editing

#1 by Rémy Sigrist at Thu Dec 15 12:32:08 EST 2022

NAME

allocated for Rémy Sigrist

KEYWORD

allocated

STATUS

approved