A036438 Integers which can be written as m*tau(m) for some m, where tau = A000005.

1, 4, 6, 10, 12, 14, 22, 24, 26, 27, 32, 34, 38, 40, 46, 56, 58, 60, 62, 72, 74, 75, 80, 82, 84, 86, 88, 94, 104, 106, 108, 118, 120, 122, 132, 134, 136, 140, 142, 146, 147, 152, 156, 158, 166, 168, 178, 184, 192, 194, 202, 204, 206, 214, 218, 220, 226, 228, 232

Offset: 1

Author

Simon Colton (simonco(AT)cs.york.ac.uk)

Keywords

• easy
• nonn

Comments

Invented by the HR concept formation program.

Examples

			10 = 5 * tau(5).
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..11329
• Simon Colton, Refactorable Numbers - A Machine Invention, J. Integer Sequences, Vol. 2 (1999), Article 99.1.2.
• Simon Colton, HR - Automatic Theory Formation in Pure Mathematics, 1998-1999. [Wayback Machine link]

Crossrefs

Cf. A000005, A001747, A036434.

Range of A038040.

Programs

Mathematica

q[k_] := AnyTrue[Divisors[k], # * DivisorSigma[0, #] == k &]; Select[Range[250], q] (* Amiram Eldar, Feb 01 2025 *)

PARI

isok(n) = {for (k=1, n, if (k*numdiv(k) == n, return (1));); return (0);} \\ Michel Marcus, Dec 09 2014

PARI

up_to = 65536;
A036438list(up_to) = { my(v=vector(up_to), m = Map()); for(n=1,#v,mapput(m,n*numdiv(n),n)); my(k=0,u=0); while((k<#v)&&(u<#v), u++; if(mapisdefined(m,u), k++; v[k] = u)); vector(k,i,v[i]); };
v036438 = A036438list(up_to);
A036438(n) = v036438[n]; \\ Antti Karttunen, Jul 18 2020