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 A174024 List of primes of the form x^2+y^2 such that tau(x^2+y^2) = bigomega(x*y) 0
 13, 17, 29, 37, 53, 101, 173, 197, 293, 677, 1373, 2213, 4493, 5333, 5477, 8837, 9413, 10613, 17957, 18773, 21317, 26573, 27893, 37253, 42437, 54293, 76733, 85853, 94253, 97973, 98597, 100493, 106277, 120413, 139133, 148997, 214373, 217157 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS bigomega(n) is the number of prime divisors of n (counted with multiplicity) (A001222) Because n = x^2+y^2 is prime, tau(n)= 2, and if we suppose x < y, then (x,y) = (2, p) with p prime or (x,y)=(1, 2q) with q prime. REFERENCES 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. J. Peters, A. Lodge and E. J. Ternouth, E. Gifford, Factor Table (n<100000) (British Association Mathematical Tables Vol.V), Burlington House/Cambridge University Press London 1935. LINKS 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]. Eric Weisstein's World of Mathematics, Distinct Prime Factors. EXAMPLE 13 = 2^2 + 3^2, bigomega(2*3) = 2. 17 = 1+4^2, bigomega(1*4) = 2. 994013 = 2^2 + 997^2, bigomega(2*997) = 2. MAPLE with(numtheory):T:=array(0..50000000):U=array(0..50000000 ): k:=1:for x from 1 to 1000 do:for y from x to 1000 do:if tau(x^2+y^2)= bigomega(x*y) and type(x^2+y^2, prime)=true then T[k]:=x^2+y^2:k:=k+1:else 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: indice:=U[n]: else fi:od:print(mini):T[ii]:= 99999999: ii:=1:mini:=T[1] :od: CROSSREFS Cf. A020882, A002313, A001222, A001221 (primes counted without multiplicity), A046660, A144494. Sequence in context: A154762 A079348 A349667 * A061381 A048520 A283407 Adjacent sequences: A174021 A174022 A174023 * A174025 A174026 A174027 KEYWORD nonn AUTHOR Michel Lagneau, Mar 05 2010 STATUS approved

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Last modified December 4 09:27 EST 2022. Contains 358556 sequences. (Running on oeis4.)