A112276 -id:A112276 - cp's OEIS frontend

A112277 Numbers m such that A112276(m) is composite.

8, 14, 20, 21, 24, 26, 32, 33, 34, 38, 44, 45, 48, 50, 54, 55, 56, 57, 62, 63, 64, 68, 74, 75, 76, 80, 81, 84, 85, 86, 90, 91, 92, 93, 94, 98, 104, 105, 110, 114, 115, 116, 117, 118, 119, 120, 122, 123, 124, 128, 132, 133, 135, 140, 141, 142, 143, 144, 145, 147, 152

Offset: 1

Reinhard Zumkeller, Sep 01 2005

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A000005, A066247, A112276.

f[1] = 1; f[n_] := Module[{m = n + 1, d = DivisorSigma[0, n]}, While[DivisorSigma[0, m] > d, m++]; m]; Select[Range[150], CompositeQ[f[#]] &] (* Amiram Eldar, Feb 03 2020 *)

A000005(a(n)) <= A000005(A112276(a(n))).

A066247(A112276(a(n))) = 1.

A079427 Least m > n having the same number of divisors as n, a(1) = 1.

Original entry on oeis.org

1, 3, 5, 9, 7, 8, 11, 10, 25, 14, 13, 18, 17, 15, 21, 81, 19, 20, 23, 28, 22, 26, 29, 30, 49, 27, 33, 32, 31, 40, 37, 44, 34, 35, 38, 100, 41, 39, 46, 42, 43, 54, 47, 45, 50, 51, 53, 80, 121, 52, 55, 63, 59, 56, 57, 66, 58, 62, 61, 72, 67, 65, 68, 729, 69, 70, 71, 75, 74, 78, 73

Offset: 1

Reinhard Zumkeller, Jan 08 2003

nonn

tau(a(n)) = tau(n) and tau(i) <> tau(n), n < i < a(n) (tau = A000005);

			Sets of divisors for n=10,11,12,13 and 14: D(10)={1,2,5,10}, D(11)={1,11}, D(12)={1,2,3,4,6,12}, D(13)={1,13}, D(14)={1,2,7,14}: therefore a(10)=14 (#D(10)=#D(14)).

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A000005, A112275, A112276.

Cf. A171937.

a[1] = 1; a[n_] := Module[{m = n+1, d=DivisorSigma[0, n]}, While[DivisorSigma[0, m] != d, m++]; m]; Array[a, 100] (* Amiram Eldar, Feb 03 2020 *)

a(n) = if (n==1, 1, my(m=n+1, nd=numdiv(n)); while(numdiv(m) != nd, m++); m); \\ Michel Marcus, Sep 14 2021

from sympy import divisors
def a(n):
    if n == 1: return 1
    divisorsn, m = len(divisors(n)), n + 1
    while len(divisors(m)) != divisorsn: m += 1
    return m
print([a(n) for n in range(1, 72)]) # Michael S. Branicky, Sep 14 2021

a(A000040(k)) = A079428(A000040(k)) = A000040(k+1), as A000005(p)=2 for primes p.

a(n) = A171937(n) + n. - Ridouane Oudra, Sep 14 2021

A112275 Smallest number greater than n having at least as many divisors as n.

Original entry on oeis.org

2, 3, 4, 6, 6, 8, 8, 10, 10, 12, 12, 18, 14, 15, 16, 18, 18, 20, 20, 24, 22, 24, 24, 30, 26, 27, 28, 30, 30, 36, 32, 36, 34, 35, 36, 48, 38, 39, 40, 42, 42, 48, 44, 45, 48, 48, 48, 60, 50, 52, 52, 54, 54, 56, 56, 60, 58, 60, 60, 72, 62, 63, 64, 66, 66, 70, 68, 70, 70, 72, 72, 84

Offset: 1

Reinhard Zumkeller, Sep 01 2005

nonn

A000005(n) <= A000005(a(n)) and A000005(k) < A000005(n) for n

A000005(2*k-1) <= A000005(2*k) for 1<=k<=22. - Corrected by Robert Israel, Jul 23 2019

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A079427, A112276.

Cf. A138171 (odd n for which a(n) > n+1).

N:= 1000: # for all terms before the first term > N
taus:= map(numtheory:-tau,[$1..N]):
for n from 1 to N do
found:= false:
for k from n+1 to N while not found do
   if taus[k]>=taus[n] then found:= true; A[n]:= k fi
od;
if not found then break fi
od:
seq(A[i],i=1..n-1); # Robert Israel, Jul 23 2019

kmax[n_] := 2 n;
a[n_] := Module[{tau = DivisorSigma[0, n], k},
     For[k = n + 1, k <= kmax[n], k++,
          If[DivisorSigma[0, k] >= tau, Return[k]]];
     Print["a(n) = k not found for n = ", n]];
Array[a, 100] (* Jean-François Alcover, Dec 15 2021 *)

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A112277 Numbers m such that A112276(m) is composite.

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A079427 Least m > n having the same number of divisors as n, a(1) = 1.

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A112275 Smallest number greater than n having at least as many divisors as n.

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