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A118883
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Smallest prime p with bigomega(p+1)=n, where bigomega(m)=A001222(m) is the number of prime divisors of m (counted with multiplicity).
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2
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2, 3, 7, 23, 31, 223, 127, 383, 1151, 3583, 5119, 6143, 8191, 129023, 73727, 245759, 131071, 917503, 524287, 5505023, 10616831, 14680063, 18874367, 109051903, 169869311, 654311423, 738197503, 2264924159, 2818572287, 3758096383, 2147483647, 24159191039
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Equivalently, smallest prime p such that p+1 is an n-almost prime. For smallest prime p such that p+1 is a squarefree n-almost prime, see A098026.
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LINKS
| Robert G. Wilson v, Table of n, a(n) for n = 1..421
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EXAMPLE
| a(4) = 23 because 23 is prime and 23+1 = 2*2*2*3 has 4 prime factors (24 is a 4-almost prime).
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MATHEMATICA
| (* copied directly from A073919 with only a sign change *) ptns[n_, 0] := If[n==0, {{}}, {}]; ptns[n_, k_] := Module[{r}, If[n<k, Return[{}]]; ptns[n, k] = 1 + Union@@ Table[ PadRight[ #, k] &/ @ ptns[n-k, r], {r, 0, k}]]; a[n_] := Module[{i, l, v}, v=Infinity; For[i=n, True, i++, l=(Times@@ Prime /@ # &)/@ ptns[i, n]; If[ Min @@ l > v, Return[v]]; minp = Min@@ Select[l - 1, ProvablePrimeQ]; If[minp < v, v = minp]]] (* First do <<NumberTheory`PrimeQ`. ptns[n, k] is list of partitions of n into exactly k parts *) (* appended by RGWv *) Array[a, 32] (* Robert G. Wilson v, 21 July 2011 *)
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CROSSREFS
| Cf. A073919, A098026, A073918.
Sequence in context: A120302 A093363 A127581 * A061712 A059661 A072686
Adjacent sequences: A118880 A118881 A118882 * A118884 A118885 A118886
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KEYWORD
| nonn
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AUTHOR
| Rick L. Shepherd (rshepherd2(AT)hotmail.com), May 03 2006
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EXTENSIONS
| a(26)-a(32) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Feb 02 2011
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