%I #11 Nov 04 2019 00:59:42
%S 12,18,20,24,28,40,44,45,48,52,56,60,68,76,80,84,88,90,92,96,99,104,
%T 108,112,116,120,124,126,132,136,140,148,152,153,156,160,162,164,168,
%U 172,176,180,184,188,192,198,204,207,208,212,220,224,228,232,234,236,240,244,248
%N Numbers N such that A328919(N) < A051903(N); numbers N such that {sigma_k(N) mod N: k >= m} is purely periodic with some m < e, where e is the maximal exponent in prime factorization of N.
%C It is easy to see that {sigma_k(N) mod N: k >= A051903(N)} is purely periodic.
%C All terms are nonsquarefree: if N is squarefree and N is here, then A328919(N) < A051903(N) = 1, so A328919(N) = 0. By the property mentioned in A328919, a necessary condition is that for every prime p dividing N, write N = p*s, we have p divides d(s), d = A000005. But d(s) is a power of 2, so N = 2, and 2 is not here.
%C Although it seems that for most N we have A328919(N) = A051903(N), this sequence is infinite. See A328934 for more information.
%e A328919(12) = 0, while A051903(12) = 2, so 12 is a term.
%e A328919(24) = 1, while A051903(24) = 3, so 24 is a term.
%e If N = p^e for prime p, then A328919(p^e) = A051903(p^e) = e. So this sequence and A000961 have empty intersection.
%o (PARI) isA328930(n) == (A328919(n)<A051903(n)) \\ See A328919 and A051903 for their program.
%Y Cf. A328919, A051903, A328934, A000961, A000005.
%K nonn
%O 1,1
%A _Jianing Song_, Oct 31 2019