A036878 -id:A036878 - cp's OEIS frontend

A120700 a(n) is the least refactorable number k having the n-th prime as its greatest prime factor.

2, 9, 40, 56, 88, 104, 136, 152, 184, 232, 248, 296, 328, 344, 376, 424, 472, 488, 536, 568, 584, 632, 664, 712, 776, 808, 824, 856, 872, 904, 1016, 1048, 1096, 1112, 1192, 1208, 1256, 1304, 1336, 1384, 1432, 1448, 1528, 1544, 1576, 1592, 1688, 1784, 1816

Offset: 1

Walter Kehowski and Robert G. Wilson v, Jun 28 2006

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A033950, A036878.

f[n_] := Block[{a = Mod[n, DivisorSigma[0, n]], b = PrimePi[FactorInteger[n][[ -1, 1]]]}, {a, b}]; t = Table[0, {100}]; Do[c = f[n]; If[c[[1]] == 0 && t[[c[[2]]]] == 0, t[[c[[2]]]] = n], {n, 2, 1831}]

A337674 Numbers k whose prime divisors are all less than or equal to the number of divisors of k.

Original entry on oeis.org

1, 2, 4, 6, 8, 9, 12, 16, 18, 20, 24, 27, 30, 32, 36, 40, 42, 45, 48, 50, 54, 56, 60, 64, 70, 72, 75, 80, 81, 84, 90, 96, 100, 105, 108, 112, 120, 126, 128, 132, 135, 140, 144, 150, 160, 162, 168, 180, 189, 192, 196, 198, 200, 210, 216, 220, 224, 225, 240, 243, 250

Offset: 1

Richard Peterson, Sep 15 2020

nonn

Density: 33 terms between 1 and 100, 17 between 201 and 300, 11 between 1001 and 1100, and 2 between 1000001 and 1000100.

			42=a(17) is a term, since 2,3 and 7 are the prime divisors of 42, which has 8 divisors. 156=2^2*3*13 is not a term, since 13 is greater than 12, the number of divisors of 156.

A199768 has "strictly less", while this sequence has "less than or equal to".
The union of A199768 and A036878.
A146982 does not include terms 42, 56, 132, 198, 220, 264, 308, 312, 330, ...
Cf. A000005.

Select[Range[250], FactorInteger[#][[-1, 1]] <= DivisorSigma[0, #] &] (* Amiram Eldar, Sep 22 2020 *)

isok(m) = #select(x->(x>numdiv(m)), factor(m)[,1]) == 0; \\ Michel Marcus, Sep 22 2020

A375790 Numbers k such that (sigma(k) - k)^(sigma(k) - k) == k (mod sigma(k)), where sigma = A000203.

Original entry on oeis.org

1, 9, 10, 112, 136, 514, 528, 625, 652, 1072, 1152, 1216, 1984, 2016, 2956, 3808, 4320, 4672, 5056, 6592, 8716, 9801, 10432, 13552, 29632, 32896, 38476, 40096, 47296, 72256, 117649, 148960, 174592, 181000, 232128, 245025, 246208, 288832, 289216, 355492, 392448, 405952, 419392, 458752, 499968

Offset: 1

Juri-Stepan Gerasimov, Aug 29 2024

nonn

			9 is in this sequence because (sigma(9)-9)^(sigma(9)-9) = (13-4)^(13-4) = 256 modulo 13 equal to 9.

Cf. A000203, A001065, A036878, A375488.

[k: k in [1..50000] | (SumOfDivisorse(k)-k)^(SumOfDivisorse(k)-k) mod SumOfDivisors(k) eq k];

isok(k) = my(s=sigma(k)); Mod(s-k, s)^(s-k) == k \\ Michel Marcus, Aug 29 2024

More terms from Michel Marcus, Aug 29 2024

cp's OEIS Frontend

A120700 a(n) is the least refactorable number k having the n-th prime as its greatest prime factor.

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A337674 Numbers k whose prime divisors are all less than or equal to the number of divisors of k.

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A375790 Numbers k such that (sigma(k) - k)^(sigma(k) - k) == k (mod sigma(k)), where sigma = A000203.

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