

A145834


a(n) = difference between the nth composite number and the sum of its prime factors with repetition.


4



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
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OFFSET

1,3


LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..2500


FORMULA

a(n) = A075255(A002808(n)) = A002808(n)  A001414(A002808(n)).


EXAMPLE

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.


MATHEMATICA

cnpf[n_]:=nTotal[Flatten[Table[#[[1]], #[[2]]]&/@FactorInteger[n]]]; cnpf/@ Select[Range[100], CompositeQ] (* Harvey P. Dale, Aug 31 2021 *)


PROG

(PARI) A145834(n)={for(k=0, primepi(n), isprime(n++)&k); n+0sum(i=1, #n=factor(n)~, n[1, i]*n[2, i])} \\ M. F. Hasler, Oct 31 2008


CROSSREFS

Cf. A001414, A002808, A075255.
Sequence in context: A159050 A210336 A280271 * A339246 A341142 A130006
Adjacent sequences: A145831 A145832 A145833 * A145835 A145836 A145837


KEYWORD

nonn


AUTHOR

Alexander R. Povolotsky, Oct 20 2008


EXTENSIONS

Edited and extended by Ray Chandler, Oct 24 2008


STATUS

approved



