



1, 3, 4, 5, 6, 8, 8, 7, 7, 10, 12, 12, 14, 12, 12, 9, 18, 13, 20, 14, 14, 16, 24, 16, 11, 18, 10, 16, 30, 20, 32, 11, 18, 22, 18, 19, 38, 24, 20, 18, 42, 22, 44, 20, 18, 28, 48, 20, 15, 17, 24, 22, 54, 18, 22, 20, 26, 34, 60, 28, 62, 36, 20, 13, 24, 26, 68, 26, 30, 26, 72, 25, 74
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OFFSET

1,2


COMMENTS

a(n) = (p+1) if n = p.


LINKS

Table of n, a(n) for n=1..73.


FORMULA

Inverse Mobius transform of A020639, where A020639 = Lpf(n): (1, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11,...). Row sums of triangle A143151.


EXAMPLE

a(4) = 5 = (1, 1, 0, 1) dot (1, 2, 3, 2) = (1 + 2 + 0 + 2), where (1, 1, 0, 1) = row 4 of triangle A051731 and A010639 = (1, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11,...).
Since a(n) = sum of least prime factors of the divisors of n, the divisors of 12 are recorded in triangle row 12 of A127093: (1, 2, 3, 4, 0, 6, 0, 0, 0, 0, 0, 12). Lpf of these terms = row 12 of triangle A143151: (1, 2, 3, 2, 0, 2, 0, 0, 0, 0, 0, 2); sum = 12.


MAPLE

read transforms : A020639 := proc(n) local i ; if n = 1 then 1; else for i from 1 do if n mod ithprime(i) = 0 then RETURN(ithprime(i)) ; fi; od: fi; end: a020639 := [seq(A020639(n), n=1..100)] : a143152 := MOBIUSi(a020639) : for i from 1 to nops(a143152) do printf("%d, ", op(i, a143152)) ; od: # R. J. Mathar, Aug 11 2008


CROSSREFS

Cf. A051731, A020639, A127093, A143151.
Sequence in context: A134338 A084919 A153100 * A229109 A096127 A327953
Adjacent sequences: A143149 A143150 A143151 * A143153 A143154 A143155


KEYWORD

nonn


AUTHOR

Gary W. Adamson, Jul 27 2008


EXTENSIONS

Extended beyond a(14) by R. J. Mathar, Aug 11 2008


STATUS

approved



