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A145834
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a(n) = difference between the n-th composite number and the sum of its prime factors with repetition.
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4
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0, 1, 2, 3, 3, 5, 5, 7, 8, 10, 11, 11, 9, 15, 15, 11, 18, 17, 20, 22, 19, 15, 23, 26, 17, 23, 29, 30, 29, 34, 21, 37, 35, 38, 31, 35, 43, 39, 43, 35, 27, 48, 29, 50, 52, 47, 50, 47, 43, 56, 60, 35, 62, 53, 59, 60, 67, 69, 39, 70, 63, 41, 55, 71, 77, 71, 65, 59, 45, 71, 83, 82, 82
(list;
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listen;
history;
text;
internal format)
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OFFSET
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1,3
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LINKS
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Harvey P. Dale, Table of n, a(n) for n = 1..2500
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FORMULA
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a(n) = A075255(A002808(n)) = A002808(n) - A001414(A002808(n)).
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EXAMPLE
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a(1) = 4 - (2+2) = 0; a(2) = 6 - (2+3) = 1; a(3) = 8 - (2+2+2) = 2 ; a(4) = 9 - (3+3) = 3; a(5) = 10 - (2+5) = 3.
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MATHEMATICA
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cnpf[n_]:=n-Total[Flatten[Table[#[[1]], #[[2]]]&/@FactorInteger[n]]]; cnpf/@ Select[Range[100], CompositeQ] (* Harvey P. Dale, Aug 31 2021 *)
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PROG
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(PARI) A145834(n)={for(k=0, primepi(n), isprime(n++)&k--); n+0-sum(i=1, #n=factor(n)~, n[1, i]*n[2, i])} \\ M. F. Hasler, Oct 31 2008
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CROSSREFS
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Cf. A001414, A002808, A075255.
Sequence in context: A159050 A210336 A280271 * A339246 A341142 A130006
Adjacent sequences: A145831 A145832 A145833 * A145835 A145836 A145837
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KEYWORD
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nonn
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AUTHOR
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Alexander R. Povolotsky, Oct 20 2008
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EXTENSIONS
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Edited and extended by Ray Chandler, Oct 24 2008
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STATUS
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approved
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