A106317 Numbers k such that the remainder of the harmonic residue of k when divided by k is k-1.
1, 2, 3, 5, 7, 11, 13, 17, 19, 21, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199
Offset: 1
Keywords
Programs
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PARI
is(n) = {my(f = factor(n)); n*numdiv(f) % sigma(f) == n - 1;} \\ Amiram Eldar, Jan 09 2024
Formula
It appears that k is in the sequence iff k is prime or k is in {1, 21, 822857} (Verified to 3.1*10^6). It is true that if k is the product of two distinct primes, then k=21. - George J. Schaeffer (gschaeff(AT)andrew.cmu.edu), Apr 30 2005, R. J. Mathar, Jan 25 2017
There are no other nonprime terms below 10^11. - Amiram Eldar, Jan 09 2024