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Search: id:A067889
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| A067889 |
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Primes sandwiched between two numbers having same number of divisors. |
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+0
3
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| 7, 19, 41, 103, 137, 199, 307, 349, 491, 739, 823, 919, 1013, 1061, 1193, 1277, 1289, 1409, 1433, 1447, 1481, 1543, 1609, 1667, 1721, 1747, 2153, 2357, 2441, 2617, 2683, 2777, 3259, 3319, 3463, 3581, 3593, 3769, 3797, 3911, 3943, 4013, 4217, 4423, 4457
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Primes p such that tau(p+1)=tau(p-1) where tau(k)=A000005(k).
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..10000
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FORMULA
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a(n) seems curiously to be asymptotic to 25*n*Log(n)
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EXAMPLE
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7 is a member as 6 and 8 both have 4 divisors; 19 is a member as 18 and 20 both have 6 divisors each.
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MAPLE
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with(numtheory):j := 0:for i from 1 to 10000 do b := ithprime(i): if nops(divisors(b-1))=nops(divisors(b+1)) then j := j+1:a[j] := b:fi:od:seq(a[k], k=1..j);
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MATHEMATICA
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Prime[ Select[ Range[ 700 ], Length[ Divisors[ Prime[ #1 ] - 1 ]] == Length[ Divisors[ Prime[ #1 ] + 1 ]] & ]]
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CROSSREFS
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Adjacent sequences: A067886 A067887 A067888 this_sequence A067890 A067891 A067892
Sequence in context: A087762 A097240 A097241 this_sequence A100620 A002177 A141193
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KEYWORD
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easy,nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 02 2002
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