A328930 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.

12, 18, 20, 24, 28, 40, 44, 45, 48, 52, 56, 60, 68, 76, 80, 84, 88, 90, 92, 96, 99, 104, 108, 112, 116, 120, 124, 126, 132, 136, 140, 148, 152, 153, 156, 160, 162, 164, 168, 172, 176, 180, 184, 188, 192, 198, 204, 207, 208, 212, 220, 224, 228, 232, 234, 236, 240, 244, 248

Offset

1,1

Comments

It is easy to see that {sigma_k(N) mod N: k >= A051903(N)} is purely periodic.

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.

Although it seems that for most N we have A328919(N) = A051903(N), this sequence is infinite. See A328934 for more information.

Links

Table of n, a(n) for n=1..59.

Example

A328919(12) = 0, while A051903(12) = 2, so 12 is a term.
A328919(24) = 1, while A051903(24) = 3, so 24 is a term.
If N = p^e for prime p, then A328919(p^e) = A051903(p^e) = e. So this sequence and A000961 have empty intersection.

Prog

(PARI) isA328930(n) == (A328919(n)<A051903(n)) \\ See A328919 and A051903 for their program.

Crossrefs

Cf. A328919, A051903, A328934, A000961, A000005.

Sequence in context: A182854 A348097 A345381 * A364996 A363082 A270660

Adjacent sequences: A328927 A328928 A328929 * A328931 A328932 A328933

Keyword

nonn

Author

Jianing Song, Oct 31 2019

Status

approved