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A114966
Prime(n) + Semiprime(n) + 3AlmostPrime(n) + 4AlmostPrime(n) + 5AlmostPrime(n).
1
62, 93, 140, 157, 214, 224, 248, 326, 344, 364, 384, 423, 451, 516, 538, 568, 589, 600, 630, 672, 689, 736, 807, 837, 871, 892, 916, 937, 964, 993, 1030, 1052, 1090, 1100, 1164, 1192, 1250, 1294, 1320, 1359, 1373, 1387, 1435, 1454, 1487, 1526, 1547, 1584
OFFSET
1,1
COMMENTS
Primes in this sequence include a(4) = 157, a(28) = 937, a(41) = 1373, a(45) = 1487, a(49) = 1609.
LINKS
FORMULA
a(n) = A000040(n) + A001358(n) + A014612(n) + A014613(n) + A014614(n). a(n) = A114944(n) + A014614(n).
EXAMPLE
a(1) = Prime(1) + Semiprime(1) + 3AlmostPrime(1) +
4AlmostPrime(1) + 5AlmostPrime(1) = 2 + 4 + 8 + 16 + 32 = 62.
a(6) = A114944(6) + A014614(6) = 112 + 112 = 224.
MATHEMATICA
Module[{nn=1000, p1, p2, p3, p4, p5, len}, p1=Prime[Range[nn]]; p2= Select[ Range[ nn], PrimeOmega[ #] ==2&]; p3=Select[ Range[nn], PrimeOmega[ #]==3&]; p4=Select[ Range[ nn], PrimeOmega[#]==4&]; p5=Select[ Range[ nn], PrimeOmega[ #]==5&]; len=Min[Length/@{p1, p2, p3, p4, p5}]; Total/@Thread[ {Take[ p1, len], Take[p2, len], Take[p3, len], Take[p4, len], Take[p5, len]}]] (* Harvey P. Dale, Apr 16 2015 *)
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Feb 21 2006
EXTENSIONS
Corrected by Harvey P. Dale, Apr 16 2015
STATUS
approved