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

1,1

Comments

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

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.

Example

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

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A393853 A295927 A059493 * A053945 A357804 A097573

Adjacent sequences: A212324 A212325 A212326 * A212328 A212329 A212330

Keyword

nonn

Author

Naohiro Nomoto, May 18 2012

Extensions

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

Status

approved