addhelp(upto, "Numbers k such that A071187(k) <> A329614(k) where k <= n."); upto(n) = { my(res = List()); for(i = 2, sqrtint(n), i2 = i^2; if(A071187(i2) != A329614(i2), listput(res, i2); ) ); res } addhelp(A329614, "Smallest prime factor of the number of divisors of A108951(n)."); A329614(n) = { if(n==1, return(1)); my(f = factor(n), res = oo); e = 1; forstep(i = #f~, 1, -1, e += f[i, 2]; res = min(res, A020639(e)); if(res == 2, return(2) ) ); res } addhelp(A020639, "Lpf(n): least prime dividing n (when n > 1); a(1) = 1. Or, smallest prime factor of n, or smallest prime divisor of n."); A020639(n) = { if(n == 1, return(1)); my(f = factor(n)); f[1,1] } addhelp(A071187, "Smallest prime factor of number of divisors of n; a(1) = 1."); A071187(n) = { A020639(numdiv(n)) }