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A056240
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Smallest number whose prime divisors add to n.
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6
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2, 3, 4, 5, 8, 7, 15, 14, 21, 11, 35, 13, 33, 26, 39, 17, 65, 19, 51, 38, 57, 23, 95, 46, 69, 92, 115, 29, 161, 31, 87, 62, 93, 124, 155, 37, 217, 74, 111, 41, 185, 43, 123, 86, 129, 47, 215, 94, 141, 188, 235, 53, 329, 106, 159, 212, 265, 59, 371, 61, 177, 122
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,1
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COMMENTS
| a(n) = index of first occurrence of n in A001414.
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LINKS
| H. Havermann: Tables of sum-of-prime-factors sequences (overview with links to the first 50000 sums).
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FORMULA
| It appears that this sequence can be computed as follows: if n is prime, a(n) = n. Otherwise, find the k with the smallest value of a(k) such that n - k is prime. Then a(n) = (n-k) * a(k). - Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Sep 15 2006
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EXAMPLE
| a(8) = 15 because the smallest number whose prime divisors sum to 8 is 15 (3*5)
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MATHEMATICA
| a = Table[0, {75}]; Do[b = Plus @@ Flatten[ Table[ #1, {#2}] & @@@ FactorInteger[n]]; If[b < 76 && a[[b]] == 0, a[[b]] = n], {n, 2, 1000}]; a (Robert G. Wilson v (rgwv(AT)rgwv.com), May 04 2002)
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CROSSREFS
| Cf. A001414, A064502.
First column of array A064364, n>=2.
See A000792 for the maximal numbers whose prime factors sums up to n.
Sequence in context: A091893 A074756 A075162 * A069968 A086931 A164339
Adjacent sequences: A056237 A056238 A056239 * A056241 A056242 A056243
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KEYWORD
| nonn,easy
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AUTHOR
| Adam Kertesz (adamkertesz(AT)worldnet.att.net), Aug 19 2000
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Aug 25 2000
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