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A065061
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Numbers k such that sigma(k) - tau(k) is a prime.
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5
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3, 8, 162, 512, 1250, 8192, 31250, 32768, 41472, 663552, 2531250, 3748322, 5120000, 6837602, 7558272, 8000000, 15780962, 33554432, 35701250, 42762752, 45334242, 68024448, 75031250, 78125000, 91125000, 137149922, 243101250, 512000000, 907039232, 959570432
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OFFSET
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1,1
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COMMENTS
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Terms greater than 3 must be twice a square (see A064205).
No terms are congruent to 4 or 6 (mod 10) (see A064205).
(End)
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LINKS
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EXAMPLE
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162 is a term since sigma(162) - tau(162) = 363 - 10 = 353, which is prime.
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MATHEMATICA
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Do[ If[ PrimeQ[ DivisorSigma[1, n] - DivisorSigma[0, n]], Print[n]], {n, 1, 10^7}]
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PROG
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(PARI) { n=0; for (m=1, 10^9, if (isprime(sigma(m) - numdiv(m)), write("b065061.txt", n++, " ", m); if (n==100, return)) ) } \\ Harry J. Smith, Oct 05 2009
(Python)
from itertools import count, islice
from sympy import isprime, divisor_sigma as s, divisor_count as t
def agen(): # generator of terms
yield 3
yield from (k for k in (2*i*i for i in count(1)) if isprime(s(k)-t(k)))
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CROSSREFS
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Cf. A000005, A000203, A023194, A038344, A055813, A062700, A115919, A141242, A229264, A229265, A229266, A229268.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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