A348956 -id:A348956 - cp's OEIS frontend

A348952 a(n) = -Sum_{d|n, d < sqrt(n)} (-1)^(d + n/d).

0, 1, -1, 1, -1, 2, -1, 0, -1, 2, -1, 1, -1, 2, -2, 0, -1, 3, -1, 1, -2, 2, -1, 0, -1, 2, -2, 1, -1, 4, -1, -1, -2, 2, -2, 2, -1, 2, -2, 0, -1, 4, -1, 1, -3, 2, -1, -1, -1, 3, -2, 1, -1, 4, -2, 0, -2, 2, -1, 2, -1, 2, -3, -1, -2, 4, -1, 1, -2, 4, -1, 0, -1, 2, -3, 1, -2, 4, -1, -1

Offset: 1

Ilya Gutkovskiy, Nov 04 2021

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

Cf. A048272, A056924, A228441, A258453, A305152, A333809, A348515, A348951, A348953, A348954, A348955, A348956, A010052.

Table[-DivisorSum[n, (-1)^(# + n/#) &, # < Sqrt[n] &], {n, 1, 80}]
nmax = 80; CoefficientList[Series[Sum[x^(k (k + 1))/(1 + x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

A348952(n) = -sumdiv(n,d,if((d*d)Antti Karttunen, Nov 05 2021

G.f.: Sum_{k>=1} x^(k*(k + 1)) / (1 + x^k).
For p odd prime, a(p) = a(p^2) = -1. - Bernard Schott, Nov 22 2021
a(n) = (A010052(n) - A228441(n))/2. - Ridouane Oudra, Aug 14 2025
a(n) = A010052(n) - A305152(n). - Ridouane Oudra, Aug 20 2025

A348951 a(n) = Sum_{d|n, d < sqrt(n)} (-1)^(n/d).

Original entry on oeis.org

0, 1, -1, 1, -1, 0, -1, 2, -1, 0, -1, 3, -1, 0, -2, 2, -1, 1, -1, 1, -2, 0, -1, 4, -1, 0, -2, 1, -1, 2, -1, 3, -2, 0, -2, 2, -1, 0, -2, 4, -1, 0, -1, 1, -3, 0, -1, 5, -1, 1, -2, 1, -1, 0, -2, 4, -2, 0, -1, 4, -1, 0, -3, 3, -2, 0, -1, 1, -2, 2, -1, 4, -1, 0, -3, 1, -2, 0, -1, 5

Offset: 1

Ilya Gutkovskiy, Nov 04 2021

sign

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

Cf. A048272, A056924, A113652, A228441, A333809, A348515, A348952, A348953, A348954, A348955, A348956, A258998.

Table[DivisorSum[n, (-1)^(n/#) &, # < Sqrt[n] &], {n, 1, 80}]
nmax = 80; CoefficientList[Series[Sum[(-1)^(k + 1) x^(k (k + 1))/(1 + x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

A348951(n) = sumdiv(n,d,if((d*d)Antti Karttunen, Nov 05 2021

G.f.: Sum_{k>=1} (-1)^(k + 1) * x^(k*(k + 1)) / (1 + x^k).

a(n) = A258998(n) - A348515(n). - Ridouane Oudra, Aug 21 2025

A348953 a(n) = -Sum_{d|n, d < sqrt(n)} (-1)^(d + n/d) * d.

Original entry on oeis.org

0, 1, -1, 1, -1, 3, -1, -1, -1, 3, -1, 2, -1, 3, -4, -1, -1, 6, -1, 3, -4, 3, -1, -2, -1, 3, -4, 3, -1, 11, -1, -5, -4, 3, -6, 6, -1, 3, -4, 0, -1, 12, -1, 3, -9, 3, -1, -8, -1, 8, -4, 3, -1, 12, -6, 2, -4, 3, -1, 5, -1, 3, -11, -5, -6, 12, -1, 3, -4, 15, -1, 0, -1, 3, -9, 3, -8, 12, -1, -8

Offset: 1

Ilya Gutkovskiy, Nov 04 2021

sign

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

Cf. A000593, A046897, A070039, A109506, A333810, A348608, A348951, A348952, A348954, A348955, A348956, A037213.

Table[-DivisorSum[n, (-1)^(# + n/#) # &, # < Sqrt[n] &], {n, 1, 80}]
nmax = 80; CoefficientList[Series[Sum[k x^(k (k + 1))/(1 + x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

A348953(n) = -sumdiv(n,d,if((d*d)Antti Karttunen, Nov 05 2021

G.f.: Sum_{k>=1} k * x^(k*(k + 1)) / (1 + x^k).

a(n) = A037213(n) - A348608(n). - Ridouane Oudra, Aug 21 2025

A348955 a(1) = 1; a(n) = Sum_{d|n, d <= sqrt(n)} a(d)^2.

Original entry on oeis.org

1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 2, 6, 1, 3, 1, 6, 2, 2, 1, 7, 2, 2, 2, 6, 1, 4, 1, 6, 2, 2, 2, 11, 1, 2, 2, 7, 1, 7, 1, 6, 3, 2, 1, 11, 2, 3, 2, 6, 1, 7, 2, 7, 2, 2, 1, 12, 1, 2, 3, 10, 2, 7, 1, 6, 2, 4, 1, 15, 1, 2, 3, 6, 2, 7, 1, 11, 6, 2, 1, 12, 2, 2, 2, 10, 1, 12

Offset: 1

Ilya Gutkovskiy, Nov 04 2021

nonn

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

Cf. A008578 (positions of 1's), A067868, A068108, A082588, A337135, A348956.

a[1] = 1; a[n_] := a[n] = DivisorSum[n, a[#]^2 &, # <= Sqrt[n] &]; Table[a[n], {n, 90}]

A348955(n) = if(1==n,n,sumdiv(n,d,if((d*d)<=n,A348955(d)^2,0))); \\ Antti Karttunen, Nov 05 2021

G.f.: Sum_{k>=1} a(k)^2 * x^(k^2) / (1 - x^k).

a(4^n) = A067868(n).

A348954 a(n) = Sum_{d|n, d < sqrt(n)} (-1)^(n/d) * d.

Original entry on oeis.org

0, 1, -1, 1, -1, -1, -1, 3, -1, -1, -1, 6, -1, -1, -4, 3, -1, 2, -1, -1, -4, -1, -1, 10, -1, -1, -4, -1, -1, 7, -1, 7, -4, -1, -6, 2, -1, -1, -4, 12, -1, -4, -1, -1, -9, -1, -1, 16, -1, 4, -4, -1, -1, -4, -6, 14, -4, -1, -1, 13, -1, -1, -11, 7, -6, -4, -1, -1, -4, 11, -1, 8, -1, -1, -9, -1, -8, -4, -1, 20

Offset: 1

Ilya Gutkovskiy, Nov 04 2021

sign

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

Cf. A000593, A070039, A109506, A333810, A348660, A348951, A348952, A348953, A348955, A348956.

Table[DivisorSum[n, (-1)^(n/#) # &, # < Sqrt[n] &], {n, 1, 80}]
nmax = 80; CoefficientList[Series[Sum[(-1)^(k + 1) k x^(k (k + 1))/(1 + x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

A348954(n) = sumdiv(n,d,if((d*d)Antti Karttunen, Nov 05 2021

G.f.: Sum_{k>=1} (-1)^(k + 1) * k * x^(k*(k + 1)) / (1 + x^k).

cp's OEIS Frontend

A348952 a(n) = -Sum_{d|n, d < sqrt(n)} (-1)^(d + n/d).

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A348951 a(n) = Sum_{d|n, d < sqrt(n)} (-1)^(n/d).

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Mathematica

PARI

Formula

A348953 a(n) = -Sum_{d|n, d < sqrt(n)} (-1)^(d + n/d) * d.

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Author

Keywords

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Crossrefs

Programs

Mathematica

PARI

Formula

A348955 a(1) = 1; a(n) = Sum_{d|n, d <= sqrt(n)} a(d)^2.

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Mathematica

PARI

Formula

A348954 a(n) = Sum_{d|n, d < sqrt(n)} (-1)^(n/d) * d.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula