A212490
Least number m > 1 such that A000203(x)*x = m has exactly n solutions.
Original entry on oeis.org
6, 336, 333312, 5418319872, 1584858562560
Offset: 1
For n=3, 333312 has exactly 3 solutions: sigma(434)*434 = 333312, sigma(372)*372 = 333312, and sigma(336)*336 = 333312; therefore a(3) = 333312.
- R. K. Guy, Unsolved Problems in Theory of Numbers, Springer-Verlag, Third Edition, 2004, B11.
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isok(k, n) = sumdiv(k, d, d*sigma(d) == k) == n;
a(n) = my(k=2); while (! isok(k,n), k++); k; \\ Michel Marcus, Oct 28 2020
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\\ See Corneth link. David A. Corneth, Nov 01 2020
A212327
Numbers k such that A001065(x)*x = k has at least two solutions.
Original entry on oeis.org
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
For k = 36, A001065(6)*6 = 36, A001065(9)*9 = 36, therefore 36 is a term.
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q[k_] := DivisorSum[k, 1 &, # * (DivisorSigma[1, #] - #) == k &] > 1; Select[Range[23*10^5], q] (* Amiram Eldar, Jul 01 2025 *)
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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
A212373
Numbers n such that A001065(x)*x = n has at least two solutions, where x is an abundant number.
Original entry on oeis.org
141440, 2286080, 6680960, 1119849500, 2081125376, 3991520000, 4141021500, 9644638208, 23664804800, 32662630400, 37516855536, 67994319888, 577461690368, 618169892864, 627198842816, 4132702579824, 4949713492400, 5025386326400, 5579119296000, 9013476012156
Offset: 1
Example: For n=141440, A001065(340)*340 = 141440, A001065(320)*320 = 141440, A001065(340) > 340, A001065(320) > 320, therefore 141440 is included in this sequence.
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