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A174049 Prime numbers of the form x^2+y^2 such that Mobius(x) * Mobius(y) = 1. 1
2, 13, 29, 37, 53, 101, 173, 197, 293, 421, 541, 677, 709, 1021, 1069, 1117, 1373, 1381, 1429, 1597, 1621, 1669, 1709, 1741, 1789, 1861, 1901, 1933, 2053, 2213, 2269, 2293, 2341, 2381, 2557, 2677, 2749, 2797, 3061, 3109, 3221, 3613, 3637, 3701 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

Deleglise, Marc and Rivat, Joel, Computing the summation of the Mobius function. Experiment. Math. 5 (1996), no. 4, 291-295.

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 844.

LINKS

Table of n, a(n) for n=1..44.

Primefan, Mobius and Mertens Values For n=1 to 2500

Gérard Villemin, Tables des Nombres de Moebius et de Mertens

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

EXAMPLE

2 is in the sequence because 2 = 1^2 + 1^2 and mobius(1)*mobius(1) = 1*1 = 1;

13 is in the sequence because 13 = 2^2 + 3^2 and mobius(2)*mobius(3) = (-1)*(-1) = 1;

MAPLE

with(numtheory): T:=array(0..50000000): k:=1:for x from 1 to 1000 do: for y from x to 1000 do if mobius(x)* mobius(y)= 1 and isprime(x^2+y^2) then T[k]:=x^2+y^2:k:=k+1 fi od od: mini:=T[1]:ii:=1: for p from 1 to k-1 do for n from 1 to k-1 do if T[n] < mini then mini:= T[n]:ii:=n fi od: print(mini): T[ii]:= 99999999: ii:=1:mini:=T[1] :od:

CROSSREFS

Cf. A008683.

Sequence in context: A033837 A041575 A042917 * A141336 A253970 A298392

Adjacent sequences:  A174046 A174047 A174048 * A174050 A174051 A174052

KEYWORD

nonn

AUTHOR

Michel Lagneau, Mar 06 2010

EXTENSIONS

Added punctuation to the examples. Corrected and edited by Michel Lagneau, Apr 25 2010

Typo in name and missing value inserted by D. S. McNeil, Nov 20 2010

STATUS

approved

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Last modified June 2 18:09 EDT 2020. Contains 334787 sequences. (Running on oeis4.)