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A257391
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Numbers of the form 4^p*(4^p+1)*(2^p-1) with p an odd prime.
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3
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29120, 32537600, 34093383680, 36011213418659840, 36888985097480437760, 38685331082014736871587840, 39614005699412557795646504960, 41538369916519054182462860998737920, 44601490313984496701256699111250939955118080, 45671926145323068271210017365594287580527984640
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OFFSET
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1,1
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COMMENTS
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5 divides (4^m+1) for odd m, so every term in this sequence is a multiple of 5 (A008587).
A064487(k) = 4^(2k+1)*(4^(2k+1)+1)*(2^(2k+1)-1), so this sequence is a subsequence of A064487.
Every non-solvable number (A056866) is divisible by 12 or 20. All non-solvable numbers not divisible by 12 (A008594) are divisible by a member of this sequence. In particular, every primitive non-solvable number (A257146) not divisible by 12 is in this sequence.
All terms are divisible by 320 and have at least 4 distinct prime factors. - Jianing Song, Apr 04 2022
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REFERENCES
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LINKS
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FORMULA
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PROG
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(Sage) [4^nth_prime(n)*(4^nth_prime(n)+1)*(2^nth_prime(n)-1) for n in range(2, 12)]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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