

A105221


a(n) is the sum of n's distinct prime factors below n.


11



0, 0, 0, 2, 0, 5, 0, 2, 3, 7, 0, 5, 0, 9, 8, 2, 0, 5, 0, 7, 10, 13, 0, 5, 5, 15, 3, 9, 0, 10, 0, 2, 14, 19, 12, 5, 0, 21, 16, 7, 0, 12, 0, 13, 8, 25, 0, 5, 7, 7, 20, 15, 0, 5, 16, 9, 22, 31, 0, 10, 0, 33, 10, 2, 18, 16, 0, 19, 26, 14, 0, 5, 0, 39, 8, 21, 18, 18, 0, 7, 3, 43, 0, 12, 22, 45
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OFFSET

1,4


LINKS

T. D. Noe, Table of n, a(n) for n=1..1000


FORMULA

a(n) = A008472(n)  A010051(n) * n.  Reinhard Zumkeller, Apr 05 2013
G.f.: Sum_{k>=1} prime(k) * x^(2*prime(k)) / (1  x^prime(k)).  Ilya Gutkovskiy, Apr 13 2021


EXAMPLE

a(12)=5 because 12's distinct prime factors 2 and 3 sum to 5.


MATHEMATICA

Table[Total@Select[Join@@Union@*Table@@@FactorInteger@k, #<k&], {k, 86}] (* Giorgos Kalogeropoulos, Nov 21 2021 *)


PROG

(Haskell)
a105221 n = a008472 n  n * fromIntegral (a010051 n)
 Reinhard Zumkeller, Apr 05 2013
(PARI) a(n) = my(f=factor(n)); sum(k=1, #f~, if (f[k, 1]<n, f[k, 1])); \\ Michel Marcus, Nov 21 2021


CROSSREFS

Cf. A003508, A008472, A010051.
Sequence in context: A171388 A086134 A071090 * A215339 A061376 A058974
Adjacent sequences: A105218 A105219 A105220 * A105222 A105223 A105224


KEYWORD

easy,nonn


AUTHOR

Alexandre Wajnberg, Apr 13 2005


EXTENSIONS

Edited by Don Reble, Nov 17 2005


STATUS

approved



