A082052 -id:A082052 - cp's OEIS frontend

A326048 a(n) = gcd(n-A050449(n), A082052(n)-n), where A050449 and A082052 give the sum of divisors of the form 4k+1, and not of that form, respectively.

1, 1, 2, 1, 1, 5, 6, 1, 1, 2, 10, 1, 1, 1, 3, 1, 1, 1, 18, 2, 1, 1, 22, 1, 1, 2, 1, 27, 1, 12, 30, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 4, 42, 1, 3, 5, 46, 1, 1, 1, 3, 2, 1, 4, 1, 1, 1, 2, 58, 6, 1, 1, 2, 1, 1, 4, 66, 10, 1, 4, 70, 1, 1, 2, 2, 3, 1, 4, 78, 2, 1, 2, 82, 2, 1, 5, 3, 1, 1, 6, 7, 1, 1, 1, 1, 5, 1, 1, 14, 1, 1, 12, 102, 2, 9

Offset: 1

Antti Karttunen, Jun 04 2019

nonn

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

Cf. A050449, A082052, A326047, A326049, A326050.

Cf. also A009194, A325385, A325813, A325975.

A050449(n) = sumdiv(n, d, d*((d % 4) == 1)); \\ From A050449
A326049(n) = (n-A050449(n));
A082052(n) = sumdiv(n, d, if(1!=(d%4), d));
A326050(n) = (A082052(n)-n);
A326048(n) = gcd(A326049(n), A326050(n));

a(n) = gcd(A326049(n), A326050(n)) = gcd(n-A050449(n), A082052(n)-n).

a(2n-1) = A326047(2n-1) for all n.

A326050 a(n) = A082052(n) - n, where A082052 is the sum of divisors of n that are not of the form 4k+1.

Original entry on oeis.org

-1, 0, 0, 2, -5, 5, 0, 6, -6, 2, 0, 15, -13, 9, 3, 14, -17, 11, 0, 16, -11, 13, 0, 35, -25, 2, 3, 27, -29, 36, 0, 30, -19, 2, 7, 45, -37, 21, 3, 44, -41, 32, 0, 39, -27, 25, 0, 75, -42, 12, 3, 32, -53, 56, 11, 63, -35, 2, 0, 102, -61, 33, 10, 62, -65, 44, 0, 40, -43, 68, 0, 113, -73, 2, 18, 63, -59, 76, 0, 100, -51, 2, 0, 118, -85, 45, 3

Offset: 1

Antti Karttunen, Jun 04 2019

sign

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

Cf. A033879, A082052, A326048, A326049.

Table[Total[Select[Divisors[n],Mod[#-1,4]!=0&]]-n,{n,90}] (* Harvey P. Dale, Jul 12 2024 *)

A082052(n) = sumdiv(n, d, if(1!=(d%4), d));
A326050(n) = (A082052(n)-n);

a(n) = A082052(n) - n.

a(n) = A326049(n) - A033879(n).

A082053 Sum of divisors of n that are not of the form 4k+3.

Original entry on oeis.org

1, 3, 1, 7, 6, 9, 1, 15, 10, 18, 1, 25, 14, 17, 6, 31, 18, 36, 1, 42, 22, 25, 1, 57, 31, 42, 10, 49, 30, 54, 1, 63, 34, 54, 6, 88, 38, 41, 14, 90, 42, 86, 1, 73, 60, 49, 1, 121, 50, 93, 18, 98, 54, 90, 6, 113, 58, 90, 1, 150, 62, 65, 31, 127, 84, 130, 1, 126, 70, 102, 1, 192

Offset: 1

Ralf Stephan, Apr 02 2003

a(A002145(n))=1.

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Cf. A000203, A050449, A050452, A050460, A078181, A078182, A082052.

sd[n_]:= Total[Select[Divisors[n], !IntegerQ[(# - 3) / 4]&]]; Array[sd, 100] (* Vincenzo Librandi, May 17 2013 *)

for(n=1,100,print1(sumdiv(n,d,if(d%4!=3,d))","))

G.f.: Sum_{k>=1} x^k*(1 + 2*x^k + 4*x^(3*k) + 3*x^(4*k) + 2*x^(5*k))/(1 - x^(4*k))^2. - Ilya Gutkovskiy, Sep 12 2019

cp's OEIS Frontend

A326048 a(n) = gcd(n-A050449(n), A082052(n)-n), where A050449 and A082052 give the sum of divisors of the form 4k+1, and not of that form, respectively.

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A326050 a(n) = A082052(n) - n, where A082052 is the sum of divisors of n that are not of the form 4k+1.

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A082053 Sum of divisors of n that are not of the form 4k+3.

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