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

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

Author

Reinhard Zumkeller, Jan 08 2003

Keywords

• nonn

Links

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

Crossrefs

Cf. A000005, A000040, A079427.

Programs

Mathematica

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 *)

PARI

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

Formula

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

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