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A126280 Triangle read by rows: T(k,n) is number of numbers <= 10^n that are products of k primes.

%I A126280 #13 Feb 16 2025 08:33:04
%S A126280 4,4,1,25,34,22,12,4,2,168,299,247,149,76,37,14,7,2,1229,2625,2569,
%T A126280 1712,963,485,231,105,47,22,7,3,1,9592,23378,25556,18744,11185,5933,
%U A126280 2973,1418,671,306,138,63,25,11,4,2,78498,210035,250853,198062,124465,68963
%N A126280 Triangle read by rows: T(k,n) is number of numbers <= 10^n that are products of k primes.
%C A126280 The n-th row's sum is 10^n - 1.
%H A126280 Robert G. Wilson v, <a href="/A126280/b126280.txt">Table of n, a(n) for n = 1..342</a>
%H A126280 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Semiprime.html">Semiprime</a>.
%H A126280 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AlmostPrime.html">Almost Prime</a>.
%e A126280 4 4 1
%e A126280 25 34 22 12 4 2
%e A126280 168 299 247 149 76 37 14
%e A126280 7 2
%e A126280 1229 2625 2569 1712 963 485 231
%e A126280 105 47 22 7 3 1
%e A126280 9592 23378 25556 18744 11185 5933 2973
%e A126280 1418 671 306 138 63 25 11 4 2
%e A126280 78498 210035 250853 198062 124465 68963 35585 17572
%e A126280 8491 4016 1878 865 400 179 79 35 14 7 2
%e A126280 664579 1904324 2444359 2050696 1349779 774078 409849 207207
%e A126280 101787 49163 23448 11068 5210 2406 1124 510 233 102 45 21 7 3 1
%t A126280 AlmostPrimePi[k_Integer, n_] := Module[{a, i}, a[0] = 1; If[k == 1, PrimePi[n], Sum[ PrimePi[ n/Times @@ Prime[ Array[a, k - 1]]] - a[k - 1] + 1, Evaluate[ Sequence @@ Table[{a[i], a[i - 1], PrimePi[(n/Times @@ Prime[ Array[a, i - 1]])^(1/(k - i + 1))]}, {i, k - 1}]] ]]]; (* _Eric W. Weisstein_, Feb 07 2006 *)
%t A126280 Table[ AlmostPrimePi[m, 10^n], {n, 6}, {m, Floor[Log[2, 10^n]] }] // Flatten
%Y A126280 By columns: A006880, A036352, A109251, A114106, A114453, A120047, A120048, A120049, A120050, A120051, A120052, A120053.
%Y A126280 The n-th row's sum: A002283 = 10^n -1, A116430, A126279: same array but for powers of two.
%K A126280 tabf,less,nonn
%O A126280 1,1
%A A126280 _Jonathan Vos Post_ & _Robert G. Wilson v_, Dec 22 2006