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A164977
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Numbers m such that the set {1..m} has only one nontrivial decomposition into subsets with equal element sum.
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11
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3, 4, 5, 6, 10, 13, 22, 37, 46, 58, 61, 73, 82, 106, 157, 166, 178, 193, 226, 262, 277, 313, 346, 358, 382, 397, 421, 457, 466, 478, 502, 541, 562, 586, 613, 661, 673, 718, 733, 757, 838, 862, 877, 886, 982, 997, 1018, 1093, 1153, 1186, 1201, 1213, 1237, 1282
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OFFSET
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1,1
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COMMENTS
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Numbers m such that m*(m+1)/2 has exactly two divisors >= m.
Also numbers m such that m*(m+1)/2 is the product of two primes.
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LINKS
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FORMULA
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{ m : |{d|m*(m+1)/2 : d>=m}| = 2 }.
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EXAMPLE
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10 is in the sequence, because there is only one nontrivial decomposition of {1..10} into subsets with equal element sum: {1,10}, {2,9}, {3,8}, {4,7}, {5,6}; 11|55.
13 is in the sequence with decomposition of {1..13}: {1,12}, {2,11}, {3,10}, {4,9}, {5,8}, {6,7}, {13}; 13|91.
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MAPLE
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a:= proc(n) option remember; local k;
for k from 1+ `if`(n=1, 2, a(n-1))
while not (isprime(k) and isprime((k+1)/2)
or isprime(k+1) and isprime(k/2))
do od; k
end:
seq(a(n), n=1..100);
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MATHEMATICA
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Select[Range@1304, PrimeOmega[#] + PrimeOmega[# + 1] == 3 &] (* Robert G. Wilson v, Jun 28 2010 and updated Sep 21 2018 *)
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PROG
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(PARI) is(n)=if(isprime(n), bigomega(n+1)==2, isprime(n+1) && bigomega(n)==2) \\ Charles R Greathouse IV, Sep 08 2015
(PARI) is(n)=if(n%2, isprime((n+1)/2) && isprime(n), isprime(n/2) && isprime(n+1)) \\ Charles R Greathouse IV, Mar 16 2022
(PARI) list(lim)=my(v=List()); forprime(p=3, lim, if(isprime((p+1)/2), listput(v, p))); forprime(p=5, lim+1, if(isprime(p\2), listput(v, p-1))); Set(v) \\ Charles R Greathouse IV, Mar 16 2022
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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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