A258914 Numbers k such that A258913(k) > k.

12, 18, 24, 31, 32, 42, 48, 54, 56, 60, 72, 80, 84, 90, 96, 98, 104, 108, 114, 120, 126, 128, 132, 140, 144, 152, 156, 168, 180, 182, 186, 192, 210, 216, 224, 228, 234, 240, 248, 252, 264, 270, 272, 280, 288, 294, 308, 312, 320, 324, 336, 342, 360, 372, 384

Offset: 1

Author

Jeppe Stig Nielsen, Jun 14 2015

Keywords

• nonn

Comments

The first k of the form k = 6m-1 in this sequence is 86831.

What can be said about the asymptotic distribution of this set? If f(x) is the count of members not exceeding x, how does f behave as x tends to infinity?

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000
• Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).
• Mathematics Stack Exchange, A number n which is the sum of all numbers k with sigma(k)=n?

Crossrefs

Cf. A258913, A000203, A085790.

Programs

PARI

is_a(n)=sum(k=1,n,if(sigma(k)==n,k))>n

PARI

is(k) = vecsum(invsigma(k)) > k; \\ Amiram Eldar, Dec 19 2024, using Max Alekseyev's invphi.gp