A079427 -id:A079427 - cp's OEIS frontend

A171937 Forward van Eck transform of A000005.

0, 1, 2, 5, 2, 2, 4, 2, 16, 4, 2, 6, 4, 1, 6, 65, 2, 2, 4, 8, 1, 4, 6, 6, 24, 1, 6, 4, 2, 10, 6, 12, 1, 1, 3, 64, 4, 1, 7, 2, 2, 12, 4, 1, 5, 5, 6, 32, 72, 2, 4, 11, 6, 2, 2, 10, 1, 4, 2, 12, 6, 3, 5, 665, 4, 4, 4, 7, 5, 8, 2, 12, 6, 3, 1, 16, 5, 10, 4, 32, 544, 3, 6, 6, 1, 1, 4, 14, 8, 6, 2, 6, 1, 1, 11

Offset: 1

N. J. A. Sloane, Oct 24 2010

nonn

Least positive k such that d(n) = d(n+k), or 0 if no such k exists (d = A000005). - Altug Alkan, Jul 29 2016

Michael De Vlieger, Table of n, a(n) for n = 1..10001
N. J. A. Sloane, Transforms

Cf. A000005, A171936.

Cf. A079427.

{0}~Join~Array[Block[{k = 1}, While[DivisorSigma[0, #] != DivisorSigma[0, # + k], k++]; k] &, 94, 2] (* Michael De Vlieger, Aug 19 2021 *)

a(n) = if (n==1, 0, my(m=1, nd=numdiv(n)); while(numdiv(n+m) != nd, m++); m); \\ Michel Marcus, Sep 14 2021

a(n) = A079427(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 *)

A112276 Smallest number greater than n having no more divisors than n; a(1) = 1.

Original entry on oeis.org

1, 3, 5, 5, 7, 7, 11, 9, 11, 11, 13, 13, 17, 15, 17, 17, 19, 19, 23, 21, 22, 23, 29, 25, 29, 27, 29, 29, 31, 31, 37, 33, 34, 35, 37, 37, 41, 39, 41, 41, 43, 43, 47, 45, 46, 47, 53, 49, 53, 51, 53, 53, 59, 55, 57, 57, 58, 59, 61, 61, 67, 65, 65, 65, 67, 67, 71, 69, 71, 71, 73, 73

Offset: 1

Reinhard Zumkeller, Sep 01 2005

nonn

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

A065091 (the odd primes) is a subsequence.
See A112277 for numbers m such that a(m) is composite.
Cf. A000005, A065091.
Cf. A079427, A112275.

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 *)

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

A079428 Least coprime number m > n with same number of divisors as n, a(1) = 1.

Original entry on oeis.org

1, 3, 5, 9, 7, 35, 11, 15, 25, 21, 13, 175, 17, 15, 22, 81, 19, 175, 23, 63, 22, 27, 29, 385, 49, 27, 34, 45, 31, 1001, 37, 45, 34, 35, 38, 1225, 41, 39, 46, 189, 43, 715, 47, 45, 52, 51, 53, 4375, 121, 63, 55, 63, 59, 385, 57, 135, 58, 65, 61, 7007, 67, 65, 68, 729, 69

Offset: 1

Reinhard Zumkeller, Jan 08 2003

nonn

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

Cf. A000005, A000040, A079427.

a[n_] := Module[{d = DivisorSigma[0, n], m = n + 1}, While[! CoprimeQ[m, n] || DivisorSigma[0, m] != d, m++]; m]; a[1] = 1; Array[a, 100] (* Amiram Eldar, Mar 26 2025 *)

a(n) = if(n == 1, 1, my(d = numdiv(n), m = n + 1); while(gcd(m, n) > 1 || numdiv(m) != d, m++); m); \\ Amiram Eldar, Mar 26 2025

tau(a(n)) = tau(n), where tau = A000005.

a(A000040(k)) = A079427(A000040(k)) = A000040(k+1).

A347982 a(n) is the greatest k, 0 < k < n, such that tau(k) = tau(n), or -1 if no such k exists, where tau is A000005.

Original entry on oeis.org

-1, -1, 2, -1, 3, -1, 5, 6, 4, 8, 7, -1, 11, 10, 14, -1, 13, 12, 17, 18, 15, 21, 19, -1, 9, 22, 26, 20, 23, 24, 29, 28, 27, 33, 34, -1, 31, 35, 38, 30, 37, 40, 41, 32, 44, 39, 43, -1, 25, 45, 46, 50, 47, 42, 51, 54, 55, 57, 53, -1, 59, 58, 52, -1, 62, 56, 61, 63, 65, 66, 67

Offset: 1

David James Sycamore, Sep 22 2021

sign

a(n) = -1 if and only if n is a term in A005179.

			a(1) = -1 because there is no positive number less than 1 having 1 divisor.
a(2) = -1 because 2 is the first prime.
a(3) = 2 because 2 is the greatest prime less than 3 and all primes have 2 divisors.

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

Cf. A000005, A005179, A079427, A079427, A140635.

a[1] = -1; a[n_] := Module[{k = n - 1, d = DivisorSigma[0, n]}, While[k > 0 && DivisorSigma[0, k] != d, k--]; If[k == 0, -1, k]]; Array[a, 100] (* Amiram Eldar, Sep 23 2021 *)

a(n) = my(nd=numdiv(n)); forstep(k=n-1, 1, -1, if (numdiv(k)==nd, return(k))); return(-1); \\ Michel Marcus, Sep 22 2021

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cp's OEIS Frontend

A171937 Forward van Eck transform of A000005.

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

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A112276 Smallest number greater than n having no more divisors than n; a(1) = 1.

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A079428 Least coprime number m > n with same number of divisors as n, a(1) = 1.

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A347982 a(n) is the greatest k, 0 < k < n, such that tau(k) = tau(n), or -1 if no such k exists, where tau is A000005.

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