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 A114944 a(n) = prime(n) + semiprime(n) + 3almostprime(n) + 4almostprime(n). 3
 30, 45, 68, 77, 106, 112, 128, 164, 176, 188, 204, 223, 243, 273, 286, 304, 319, 328, 350, 372, 385, 424, 439, 459, 479, 496, 511, 529, 544, 553, 580, 596, 626, 632, 668, 692, 730, 742, 753, 771, 781, 793, 823, 838, 857, 870, 887, 909, 929, 938, 974, 999 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Primes in this sequence include a(12) = 223, a(23) = 439, a(25) = 479, a(43) = 823, a(45) = 857, a(47) = 887, a(49) = 929. LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 Eric Weisstein's World of Mathematics, Almost Prime. FORMULA a(n) = A000040(n) + A001358(n) + A014612(n) + A014613(n). a(n) = A014613(n) + A114382(n). EXAMPLE a(1) = prime(1) + semiprime(1) + 3almostprime(1) + 4almostprime(1) = 2 + 4 + 8 + 16 = 30. a(6) = (prime(6) + semiprime(6) + 3almostprime(6)) + 4almostprime(6) = A114382(6) + 4almostprime(6) = 56 + 56 = 112. MATHEMATICA 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 *) AlmostPrime[k_, n_] := Block[{e = Floor[Log[2, n]], a, b}, a = 2^e; Do[b = 2^p; While[AlmostPrimePi[k, a] < n, a = a + b]; a = a - b/2, {p, e, 0, -1}]; a + b/2]; Table[ Sum[ AlmostPrime[k, n], {k, 4}], {n, 52}] (* Robert G. Wilson v, Feb 21 2006 *) nn=500; Module[{p=Prime[Range[nn]], p2=Select[Range[nn], PrimeOmega[#] == 2&], p3=Select[Range[nn], PrimeOmega[#] ==3&], p4 =Select[Range[nn], PrimeOmega[#]==4&], len}, len=Min[Length/@{p, p2, p3, p4}]; Total/@Thread[ {Take[p, len], Take[p2, len], Take[p3, len], Take[p4, len]}]] (* Harvey P. Dale, Jul 13 2012 *) CROSSREFS Cf. A000040, A001358, A014612, A014613, A114382. Sequence in context: A062385 A164803 A152569 * A075290 A281919 A004222 Adjacent sequences: A114941 A114942 A114943 * A114945 A114946 A114947 KEYWORD easy,nonn AUTHOR Jonathan Vos Post, Feb 20 2006 EXTENSIONS Corrected by Harvey P. Dale, Jul 13 2012 STATUS approved

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Last modified August 11 01:05 EDT 2024. Contains 375059 sequences. (Running on oeis4.)