A385757 a(n) is the smallest number having n smaller numbers with the same number of prime factors (counted with multiplicity).
3, 5, 7, 11, 13, 17, 19, 23, 26, 31, 34, 35, 38, 39, 46, 49, 51, 55, 57, 58, 62, 65, 69, 74, 77, 82, 85, 86, 87, 91, 93, 94, 95, 106, 111, 115, 118, 119, 121, 122, 123, 129, 133, 134, 141, 142, 143, 145, 146, 155, 158, 159, 161, 166, 169, 177, 178, 183, 185, 187, 194, 201, 202, 203, 205
Offset: 1
Keywords
Examples
The smallest number having 9 smaller numbers (4, 6, 9, 10, 14, 15, 21, 22 and 25) with the same number of prime factors (counted with multiplicity) is 26, so a(9) is 26.
Links
- Eric Weisstein's World of Mathematics, Prime Factor.
Programs
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Mathematica
a[n_]:=Module[{k = 1, m, cnt}, While[True,m = PrimeOmega[k];cnt = Sum[Boole[PrimeOmega[i] == m], {i, 2, k - 1}];If[cnt == n, Return[k]];k++ ]];Array[a,65] (* James C. McMahon, Jul 13 2025 *) -
PARI
a(n) = my(k=2, m=bigomega(k)); while (sum(i=2, k-1, bigomega(i) == m) !=n, k++; m=bigomega(k)); k; \\ Michel Marcus, Jul 09 2025
Comments