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A211678 Twin primes p, p+2 with unique values of sigma(p) and sigma(p+2); sigma(n) = A000203(n) = sum of divisors of n. 2
3, 5, 7, 197, 199, 281, 283, 347, 349, 461, 463, 641, 643, 821, 823, 857, 859, 1289, 1291, 1697, 1699, 1721, 1723, 1787, 1789, 1877, 1879, 2081, 2083, 2141, 2143, 2381, 2383, 2549, 2551, 2801, 2803, 3257, 3259, 3539, 3541, 3557, 3559, 3929, 3931, 4019, 4021 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Subsequence of A211656 and A211660.

LINKS

Table of n, a(n) for n=1..47.

EXAMPLE

Twin primes 197 and 199 are in sequence because sigma(197) = 198, sigma(199) = 200 and there are no other numbers m, n with sigma(m) = 198 or sigma(n) = 200.

MATHEMATICA

d = DivisorSigma[1, Range[4100]]; t = Transpose[Select[Tally[Sort[d]], #[[2]] == 1 && #[[1]] <= Length[d] &]][[1]]; t2 = Sort[Flatten[Table[Position[d, i], {i, t}]]]; t3 = Select[t2, PrimeQ]; tp = {}; Do[If[t3[[i + 1]] - t3[[i]] == 2 && DivisorSigma[1, t3[[i]]] != DivisorSigma[1, t3[[i + 1]]], AppendTo[tp, t3[[i]]]; AppendTo[tp, t3[[i]] + 2]], {i, Length[t3] - 1}]; Union[tp] (* T. D. Noe, Apr 26 2012 *)

CROSSREFS

Cf. A211767 (lesser of twin primes p, p+2 with unique values of sigma(p) and sigma(p+2), A211769 (greater of twin primes p, p+2 with unique values of sigma(p) and sigma(p+2).

Sequence in context: A114366 A088092 A174271 * A082756 A268693 A068832

Adjacent sequences:  A211675 A211676 A211677 * A211679 A211680 A211681

KEYWORD

nonn

AUTHOR

Jaroslav Krizek, Apr 20 2012

STATUS

approved

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Last modified December 5 23:38 EST 2021. Contains 349558 sequences. (Running on oeis4.)