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A353552
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Primes p such that Sum_{k=PreviousPrime(p)..p} d(k) = Sum_{k=p..NextPrime(p)} d(k), where d(k) is the number of divisors function A000005.
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4
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1871, 2141, 2677, 2777, 2903, 2963, 3673, 4969, 5107, 5417, 6323, 7487, 10459, 11173, 11497, 11689, 14519, 18047, 18077, 19081, 19379, 20357, 20533, 20611, 21577, 22619, 25621, 32621, 34543, 35531, 36821, 39089, 39503, 40111, 40771, 44263, 44647, 44917, 51551, 52181
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OFFSET
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1,1
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COMMENTS
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It doesn't matter if terms or the neighboring primes are included in the sums or excluded as long as the symmetry is taken into account.
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LINKS
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EXAMPLE
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a(2) = 2141 (a prime); previous prime is 2137; next prime is 2143.
The numbers of divisors between are:
+ d(2138) = 4 + d(2142) = 24
+ d(2139) = 8
+ d(2140) = 12
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sum = 24 sum = 24 Sums are equal. Thus 2141 is a term.
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MATHEMATICA
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Select[Prime[Range[5000]], Total[DivisorSigma[0, Range[NextPrime[#, -1], #]]] == Total[DivisorSigma[0, Range[#, NextPrime[#]]]] &] (* Amiram Eldar, May 11 2022 *)
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PROG
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(Python)
def sotsb(a, b): return sum(A000005(n) for n in range(a+1, b))
# sotsb stands for the "sum of taus strictly between (a and b)"
(PARI) isok(p) = isprime(p) && sum(k=precprime(p-1), p, numdiv(k)) == sum(k=p, nextprime(p+1), numdiv(k)); \\ Michel Marcus, May 11 2022
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CROSSREFS
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Cf. A353553 (sum of three sets are equal), A353554 (sum of four sets are equal).
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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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