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Search: id:A133855
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| A133855 |
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Primes p such that p-1 and p+1 are abundant numbers. |
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+0
1
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| 19, 41, 71, 79, 89, 101, 103, 113, 139, 197, 199, 223, 271, 281, 307, 349, 353, 367, 379, 401, 439, 449, 461, 463, 491, 499, 521, 571, 607, 617, 619, 641, 643, 701, 727, 739, 761, 769, 811, 821, 859, 881, 911, 919, 929, 941, 953, 967, 991, 1039, 1061, 1063
(list; graph; listen)
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OFFSET
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1,1
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EXAMPLE
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19-1=18=2*3*3, s/n=39/18>2, 18 is abundant,
19+1=20=2*2*5, s/n=42/20>2, 20 is abundant, so a(1)=19
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MAPLE
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with(numtheory): a:=proc(n) if isprime(n)=true and 0<sigma(n-1)-2*n+2 and 0< sigma(n+1)-2*n-2 then n else end if end proc: seq(a(n), n=2..1000); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 26 2008
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MATHEMATICA
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Select[Prime[Range[500]], (Plus @@ Divisors[ # - 1]) > 2*(# - 1) && (Plus @@ Divisors[ # + 1]) > 2*(# + 1) &] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Jan 21 2008
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CROSSREFS
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Adjacent sequences: A133852 A133853 A133854 this_sequence A133856 A133857 A133858
Sequence in context: A049485 A019393 A029489 this_sequence A094841 A001986 A095101
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KEYWORD
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nonn
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AUTHOR
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Pierre CAMI (pierrecami(AT)tele2.fr), Jan 07 2008
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EXTENSIONS
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Corrected and extended by Stefan Steinerberger (stefan.steinerberger(AT)gmail.com) and Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 21 2008
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