A057921 -id:A057921 - cp's OEIS frontend

A057922 d(n) divides d(n+1), where d(n) is number of positive divisors of n.

1, 2, 5, 7, 11, 13, 14, 17, 19, 21, 23, 26, 29, 31, 33, 34, 37, 38, 39, 41, 43, 44, 47, 49, 53, 55, 57, 59, 61, 65, 67, 69, 71, 73, 75, 77, 79, 83, 85, 86, 87, 89, 93, 94, 95, 97, 98, 101, 103, 104, 107, 109, 113, 116, 118, 119, 122, 125, 127, 129, 131, 133, 134, 135

Offset: 0

Leroy Quet, Nov 11 2000

nonn

			11 is included because d(11) = 2 divides d(12) = 6.

Ivan Neretin, Table of n, a(n) for n = 0..10000

Cf. A057921, A005237.

Select[Range@150, Divisible @@ DivisorSigma[0, {# + 1, #}] &] (* Ivan Neretin, May 29 2015 *)
Position[Partition[DivisorSigma[0,Range[150]],2,1],?(Divisible[#[[2]], #[[1]]]&),1,Heads->False]//Flatten (* _Harvey P. Dale, May 08 2019 *)

A060778 a(n) = gcd(tau(n+1), tau(n)), where tau = A000005.

Original entry on oeis.org

1, 2, 1, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 4, 1, 1, 2, 2, 2, 2, 4, 2, 2, 1, 1, 4, 2, 2, 2, 2, 2, 2, 4, 4, 1, 1, 2, 4, 4, 2, 2, 2, 2, 6, 2, 2, 2, 1, 3, 2, 2, 2, 2, 4, 4, 4, 4, 2, 2, 2, 2, 2, 1, 1, 4, 2, 2, 2, 4, 2, 2, 2, 2, 2, 6, 2, 4, 2, 2, 5, 1, 2, 2, 4, 4, 4, 4, 2, 2, 4, 2, 2, 4, 4, 4, 2, 2, 6, 3, 1, 2, 2, 2, 8, 4

Offset: 1

Labos Elemer, Apr 26 2001

nonn

Harry J. Smith, Table of n, a(n) for n=1..1000

Cf. A000005, A057921, A058074.

GCD@@@Partition[DivisorSigma[0,Range[110]],2,1] (* Harvey P. Dale, May 27 2014 *)

a(n) = gcd(numdiv(n), numdiv(n+1)); \\ Michel Marcus, Jan 12 2018

from math import gcd
from sympy import divisor_count
def A060778(n): return gcd(divisor_count(n+1),divisor_count(n)) # Chai Wah Wu, Aug 12 2023

a(n) = gcd(A000005(n+1), A000005(n)).

A060779 a(n) = lcm(tau(n+1), tau(n)), where tau = A000005.

Original entry on oeis.org

2, 2, 6, 6, 4, 4, 4, 12, 12, 4, 6, 6, 4, 4, 20, 10, 6, 6, 6, 12, 4, 4, 8, 24, 12, 4, 12, 6, 8, 8, 6, 12, 4, 4, 36, 18, 4, 4, 8, 8, 8, 8, 6, 6, 12, 4, 10, 30, 6, 12, 12, 6, 8, 8, 8, 8, 4, 4, 12, 12, 4, 12, 42, 28, 8, 8, 6, 12, 8, 8, 12, 12, 4, 12, 6, 12, 8, 8, 10, 10, 20, 4, 12, 12, 4, 4, 8, 8, 12

Offset: 1

Labos Elemer, Apr 26 2001

nonn

Harry J. Smith, Table of n, a(n) for n = 1..1000

Cf. A057921, A000005.

LCM@@#&/@Partition[DivisorSigma[0,Range[90]],2,1] (* Harvey P. Dale, Jan 27 2025 *)

a(n) = { lcm(numdiv(n), numdiv(n+1)) } \\ Harry J. Smith, Jul 11 2009

a(n) = lcm(A000005(n+1), A000005(n)).

cp's OEIS Frontend

A057922 d(n) divides d(n+1), where d(n) is number of positive divisors of n.

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A060778 a(n) = gcd(tau(n+1), tau(n)), where tau = A000005.

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Formula

A060779 a(n) = lcm(tau(n+1), tau(n)), where tau = A000005.

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Mathematica

PARI

Formula