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A065997
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Numbers n such that sigma(n) / n is prime.
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11
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6, 28, 120, 496, 672, 8128, 523776, 33550336, 459818240, 1476304896, 8589869056, 14182439040, 31998395520, 51001180160, 137438691328, 518666803200, 13661860101120, 30823866178560, 740344994887680, 796928461056000, 212517062615531520, 2305843008139952128
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OFFSET
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1,1
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COMMENTS
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This is a subsequence of the sequence of multiply perfect numbers A007691.
The prime values of sigma(n) / n are A219545.
Numbers whose abundancy index is a prime. There are two visible bends (sudden changes in the growth rate) in the scatter plot. Compare also to the scatter plot of A336702. - Antti Karttunen, Feb 25 2022
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LINKS
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PROG
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(PARI) isA065997(n) = { my(p=sigma(n)/n); (1==denominator(p) && isprime(p)); }; \\ Antti Karttunen, Feb 25 2022
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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