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A343418
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Primes that occur in A343416.
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2
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11, 29, 41, 61, 73, 97, 131, 137, 139, 149, 151, 157, 167, 179, 191, 211, 227, 229, 233, 241, 251, 283, 293, 307, 313, 331, 347, 373, 383, 389, 397, 401, 449, 463, 521, 577, 607, 631, 641, 647, 653, 661, 673, 677, 701, 709, 719, 727, 757, 769, 811, 821, 823, 829, 857, 859, 877, 887, 907, 919, 929
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OFFSET
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1,1
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COMMENTS
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Terms are distinct and in numerical order, not the order they occur in A343416.
If p, 6*p-1 and 19*p+4 are prime, then 19*p+4 = A343416(6*p-1) is a term. Dickson's conjecture implies that there are infinitely many such terms.
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LINKS
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EXAMPLE
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a(3) = 41 is a term because 41 = A343416(8) = A343416(10) and is prime.
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MAPLE
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spf:= proc(n) local t; add(t[1]*t[2], t=ifactors(n)[2]) end proc:
f:= proc(n) local a, b;
a:= spf(n);
b:= numtheory:-sigma(n);
a+b+spf(b)+numtheory:-sigma(a)
end proc:
S:= select(t -> t < 1000 and isprime(t), map(f, {$1..1000})):
sort(convert(S, list));
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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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