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Search: id:A110585
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| A110585 |
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Smallest number k of consecutive primes > p_n such that p_n^2 * p_(n+1) * p_(n+2) * ... * p_(n+k) is an abundant number. |
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+0
4
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| 1, 3, 7, 16, 29, 44, 65, 89, 120, 155, 192, 236, 282, 332, 390, 453, 520, 589, 666, 746, 832, 927, 1026, 1131, 1239, 1350, 1467, 1592, 1725, 1867, 2017, 2161, 2313, 2469, 2634, 2800, 2975, 3155, 3339, 3532, 3729, 3931, 4143, 4356, 4579, 4809, 5051, 5291
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The sequence arose while solving puzzle 329 from Carlos Rivera's Prime puzzles site.
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LINKS
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Carlos Rivera, Puzzle 329. Odd abundant numbers not divided by 2 or 3.
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EXAMPLE
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a(2)=3 because the second prime being 3, then 3^2 * 5 * 7 * 11 = 3465 and
sigma(3465) - 2*3465 = 558, a positive number, but
3^2 * 5 * 7 = 315 and sigma(315) - 2*315 = -6, a non-positive number.
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MATHEMATICA
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abQ[n_] := DivisorSigma[1, n] > 2n; f[0] = 0; f[n_] := f[n] = Block[{k = f[n - 1]}, p = Fold[Times, Prime[n], Prime[ Range[n, n + k]]]; While[ !abQ[p], k++; p = p*Prime[n + k]]; k]; Table[ f[n], {n, 48}] (* Robert G. Wilson v *)
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PROGRAM
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(PARI) forprime(p=2, 100, k=0; while(k++, if(sigma(n=p^2*prod(j=1, k, prime(j+primepi(p))))-n>n, print(k); break)))
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CROSSREFS
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Cf. A005101.
Sequence in context: A116040 A036666 A117491 this_sequence A000412 A161810 A084631
Adjacent sequences: A110582 A110583 A110584 this_sequence A110586 A110587 A110588
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KEYWORD
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nonn
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AUTHOR
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Igor Schein (igor(AT)txc.com), Sep 13 2005
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EXTENSIONS
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Edited and extended by Robert G. Wilson v (rgwv(at)rgwv.com), Sep 15 2005
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