A329307 Define b(D) = -Sum_{i=1..D} Kronecker(-D,i)*i for D == 0 or 3 (mod 4); sequence gives D such that b(D) = 0 and b(D/k^2) != 0 for k > 1, given that D/k^2 is an integer == 0 or 3 (mod 4).
28, 60, 72, 92, 99, 100, 124, 147, 156, 180, 188, 207, 220, 275, 284, 315, 316, 348, 380, 412, 423, 444, 475, 476, 504, 507, 508, 531, 572, 600, 604, 612, 636, 639, 668, 676, 732, 747, 764, 775, 796, 847, 855, 860, 892, 924, 931, 936, 956, 963, 968, 975, 980, 988, 1020
Offset: 1
Keywords
Examples
60 is a term because 60 = 2^2 * 15 and -15 is a fundamental discriminant. Indeed, -Sum_{i=1..60} Kronecker(-60,i)*i = 0 and -Sum_{i=1..15} Kronecker(-15,i)*i != 0.
Although -Sum_{i=1..252} Kronecker(-252,i)*i = 0, 252 is not a term, because 252/3^2 = 28 and -Sum_{i=1..28} Kronecker(-28,i)*i = 0
Programs
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PARI
isA329307(n) = if(n%4==0||n%4==3, my(f=factor(n)); for(i=1, omega(n), my(p=f[i,1],e=f[i,2],m=n/p^e); if(e==2 && isfundamental(-m) && kronecker(-m,p)==1, return(1)))); 0
Comments