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
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.
A212489
Numbers n such that A001065(x)*x = n has at least two solutions, where x is a deficient number.
Original entry on oeis.org
1245335, 318047135, 358491735, 533718135, 709131500, 1122571695, 1814416175, 3565970135, 4486354631, 14336906175, 14827262351, 22805269551, 36360557831, 43971297884, 72370166375, 99254203895, 102204949847, 145262865020, 156161459559, 173741271935, 231267964895
Offset: 1
Example: For n=1245335, A001065(1955)*1955 = 1245335, A001065(2093)*2093 = 1245335, A001065(1955) < 1955, A001065(2093) < 2093, therefore 1245335 is included in this sequence.
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