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

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

Author

Reinhard Zumkeller, Sep 01 2005

Keywords

• nonn

Links

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

Crossrefs

A065091 (the odd primes) is a subsequence.

See A112277 for numbers m such that a(m) is composite.

Cf. A000005, A065091.

Cf. A079427, A112275.

Programs

Mathematica

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 *)

Formula

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