A159886 Values k such that sigma(x) = k has more than one solution, sigma = A000203.

12, 18, 24, 31, 32, 42, 48, 54, 56, 60, 72, 80, 84, 90, 96, 98, 104, 108, 114, 120, 124, 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, 378, 384, 390

Offset: 1

Author

Jaroslav Krizek, Apr 25 2009

Keywords

• nonn

Comments

Numbers k with A054973(k) >= 2. Numbers k which occur in A000203 more than once.

Numbers k = A007609(n) with A007609(n+1) - A007609(n) = 0.

Does this sequence have finite density? - Franklin T. Adams-Watters, Jun 18 2009

See A300869 for the odd terms, much less frequent since they can only occur for x = k^2 or 2*k^2. - M. F. Hasler, Mar 16 2018

Examples

			a(1) = 12 as the multiplicity of the value 12 is 2: 12 = sigma(6) = sigma(11).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1095 from Franklin T. Adams-Watters)
• Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).

Crossrefs

Cf. A000203, A054973, A007609, A007368.

Subsequence of A002191.

Odd terms are listed in A300869.

Programs

PARI

na(n) = local(v, s); v=vector(n);for(k=1,n,s=sigma(k);if(s<=n,v[s]++));v
la(n) = local(v, r); v=na(n);r=[];for(k=1,n,if(v[k]>1,r=concat(r,[k])));r \\ Franklin T. Adams-Watters, Jun 18 2009

PARI

is(k) = invsigmaNum(k) > 1; \\ Amiram Eldar, Dec 16 2024, using Max Alekseyev's invphi.gp

Extensions

Edited and extended by R. J. Mathar, Apr 28 2009