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A248963
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Prime powers p^m for which sigma(p^2m) is not prime.
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2
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1, 7, 9, 11, 13, 16, 19, 23, 25, 29, 31, 32, 37, 43, 47, 53, 61, 67, 73, 79, 81, 83, 97, 103, 107, 109, 113, 121, 127, 128, 137, 139, 149, 151, 157, 163, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 243, 251, 257, 263, 269, 271, 277, 281, 283, 307, 311, 313, 317, 331
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OFFSET
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1,2
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COMMENTS
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sigma(x) cannot be prime unless x is a square of a prime power, x = p^2m, cf. A055638 and A023194. This sequence lists the complement: prime powers whose square does not have a prime sum of divisors.
Although generally 1 is not considered a prime power, it seemed logical for various good reasons to include the initial term a(1)=1.
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LINKS
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FORMULA
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PROG
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(PARI) for(n=1, 999, isprimepower(n)||next; isprime(sigma(n^2))||print1((n)", "))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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