A212327 Numbers k such that A001065(x)*x = k has at least two solutions.

36, 62480, 141440, 1245335, 1432640, 2286080, 6680960, 7660880, 27931280, 39685376, 116636864, 179299575, 318047135, 318523136, 358491735, 533718135, 709131500, 1119849500, 1122571695, 1814416175, 2081125376, 3565970135, 3991520000, 4141021500, 4483640576

Offset: 1

Author

Naohiro Nomoto, May 18 2012

Keywords

• nonn

Comments

Products of pairs of amicable numbers are members of this sequence.

Examples

			For k = 36, A001065(6)*6 = 36, A001065(9)*9 = 36, therefore 36 is a term.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..51 (terms below 10^11)
• Passawan Noppakaew and Prapanpong Pongsriiam, Product of Some Polynomials and Arithmetic Functions, J. Int. Seq., Vol. 26 (2023), Article 23.9.1.

Crossrefs

Cf. A001065, A063990, A212373, A212489, A212490.

Programs

Mathematica

q[k_] := DivisorSum[k, 1 &, # * (DivisorSigma[1, #] - #) == k &] > 1; Select[Range[23*10^5], q] (* Amiram Eldar, Jul 01 2025 *)

PARI

isok(k) = {my(d = divisors(k, 1), c = 0); for(i = 1, #d, if(d[i][1] * (sigma(d[i][2]) - d[i][1]) == k, c++; if(c == 2, break))); c == 2;} \\ Amiram Eldar, Jul 01 2025

Extensions

a(9)-a(25) from Donovan Johnson, May 21 2012