

A367734


Numbers that have no balanced divisors except for 1.


1



1, 5, 7, 11, 13, 17, 19, 23, 25, 29, 31, 37, 41, 43, 47, 49, 53, 55, 59, 61, 65, 67, 71, 73, 77, 79, 83, 85, 89, 91, 95, 97, 101, 103, 107, 109, 113, 115, 119, 121, 125, 127, 131, 133, 137, 139, 143, 145, 149, 151, 155, 157, 161, 163, 167, 169, 173, 179, 181, 185, 187, 191, 193, 197, 199, 203
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OFFSET

1,2


COMMENTS

Numbers k such that A351112(k) = 1.
Includes all primes except for 2 and 3, and all powers of those primes.
If k is a term, then so are all divisors of k.
For i < 271, a(i+68) = a(i) + 210, and this equation seems to be true for most i.


LINKS



FORMULA



EXAMPLE

a(9) = 25 is a term because of its divisors 1, 5, 25, only 1 is balanced.


MAPLE

filter:= proc(n) uses numtheory;
andmap(t > sigma(t) mod phi(t) <> 0, divisors(n) minus {1})
end proc:
select(filter, [$1..1000]);


MATHEMATICA

Select[Range[200], DivisorSum[#, 1 &, Divisible[DivisorSigma[1, #1], EulerPhi[#1]] &] == 1 &] (* Amiram Eldar, Nov 28 2023 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



