A048586 -id:A048586 - cp's OEIS frontend

A070010 GCD of consecutive values of sum-of-proper divisors.

1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 11, 1, 1, 1, 6, 2, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 4, 1, 1, 1, 23, 1, 1, 1, 1, 3, 1, 1, 5, 25, 1, 1, 1, 1, 3, 1, 1, 1, 1

Offset: 1

Labos Elemer, Apr 11 2002

nonn

Antti Karttunen, Table of n, a(n) for n = 1..10000

Cf. A000203, A001065; GCD of various consecutive function values: A048586, A057467, A058515, A060778, A060780, A069896.

GCD[DivisorSigma[1, n+1]-(n+1), DivisorSigma[1, n]-n]

A001065(n) = (sigma(n) - n);
A070010(n) = gcd(A001065(n),A001065(1+n)); \\ Antti Karttunen, Oct 05 2017

a(n) = gcd(A001065(n+1), A001065(n)).

A277089 Pisot sequences L(6,15), S(6,15).

Original entry on oeis.org

6, 15, 38, 97, 248, 635, 1626, 4164, 10664, 27311, 69945, 179134, 458775, 1174956, 3009148, 7706648, 19737289, 50548641, 129458768, 331553377, 849132458, 2174690356, 5569541124, 14264002343, 36531153701, 93558957622, 239611336203, 613662164440, 1571633704952

Offset: 0

Ilya Gutkovskiy, Sep 29 2016

Ilya Gutkovskiy, Pisot sequences L(x,y)
Index entries for Pisot sequences

Cf. See A008776 for definitions of Pisot sequences.

Cf. A020717, A048585, A048586, A048587.

RecurrenceTable[{a[0] == 6, a[1] == 15, a[n] == Ceiling[a[n - 1]^2/a[n - 2]]}, a, {n, 28}]
RecurrenceTable[{a[0] == 6, a[1] == 15, a[n] == Floor[a[n - 1]^2/a[n - 2] + 1]}, a, {n, 28}]

a(n) = ceiling(a(n-1)^2/a(n-2)), a(0) = 6, a(1) = 15.
a(n) = floor(a(n-1)^2/a(n-2)+1), a(0) = 6, a(1) = 15.
Conjectures: (Start)
G.f.: (6 - 3*x - x^2 - 2*x^3 + x^4 + 3*x^5 - 5*x^6)/((1 - x)*(1 - 2 x - x^2 - x^3 - 2*x^6)).
a(n) = 3*a(n-1) - a(n-2) - a(n-4) + 2*a(n-6) - 2*a(n-7). (End)

cp's OEIS Frontend

A070010 GCD of consecutive values of sum-of-proper divisors.

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