A344272
a(n) is the least k such that the average number of nonunitary divisors of {1..k} is >= n.
Original entry on oeis.org
54, 816, 10530, 135200, 1733760, 22216752, 284685408, 3647978320, 46745561100, 599002268832, 7675674748560
Offset: 1
a(1) = 54 since the average of the number of nonunitary divisors of {1..54} is (Sum_{k=1..54} A056175(k))/54 = 1.
-
nd[n_] := DivisorSigma[0,n] - 2^PrimeNu[n]; seq={}; s = 0; k = 1; Do[While[s = s + nd[k]; s < k*n, k++]; AppendTo[seq, k]; k++, {n, 1, 5}]; seq
A344273
a(n) is the least k such that the average number of bi-unitary divisors of {1..k} is >= n.
Original entry on oeis.org
1, 6, 24, 80, 273, 960, 3336, 11480, 39648, 136952, 472416, 1630164, 5625480, 19412736, 66992016, 231184800, 797806152, 2753187210, 9501109380, 32787848746
Offset: 1
a(2) = 6 since the average number of bi-unitary divisors of {1..6} is A306069(6)/6 = 13/6 > 2.
-
f[p_, e_] := If[OddQ[e], e + 1, e]; bdivnum[1] = 1; bdivnum[n_] := Times @@ (f @@@ FactorInteger[n]); seq={}; s = 0; k = 1; Do[While[s = s + bdivnum[k]; s < k*n, k++]; AppendTo[seq, k]; k++, {n, 1, 10}]; seq
A344274
a(n) is the least k such that the average number of infinitary divisors of {1..k} is >= n.
Original entry on oeis.org
1, 6, 24, 105, 385, 1554, 6063, 23688, 92610, 362112, 1416360, 5539296, 21663378, 84725487, 331362185, 1295952084, 5068450464, 19822658688
Offset: 1
a(2) = 6 since the average number of infinitary divisors of {1..6} is A327573(6)/6 = 13/6 > 2.
-
f[p_, e_] := 2^DigitCount[e, 2, 1]; idivnum[1] = 1; idivnum[n_] := Times @@ (f @@@ FactorInteger[n]); seq={}; s = 0; k = 1; Do[While[s = s + idivnum[k]; s < k*n, k++]; AppendTo[seq, k]; k++, {n, 1, 10}]; seq
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