A342106 Numbers that are not arithmetic and not balanced.

4, 8, 9, 10, 16, 18, 24, 25, 26, 28, 32, 34, 36, 40, 48, 50, 52, 58, 63, 64, 72, 74, 75, 76, 80, 81, 82, 84, 88, 90, 98, 100, 104, 106, 108, 112, 117, 120, 121, 122, 124, 128, 130, 136, 144, 146, 148, 152, 156, 160, 162, 170, 171, 172, 175, 176, 178, 180, 192, 194, 196, 200

Offset

1,1

Comments

Equivalently, numbers m such that neither tau(m) (A000005) nor phi(m) (A000010) divide sigma(m) (A000203).

A342103, A342104, A342105 and this sequence form a partition of the set of positive integers N* (A000027).

There are no primes in the sequence since 2 is in A342104, 3 is in A342103, and odd primes >= 5 are in A342105.

Links

Table of n, a(n) for n=1..62.

Example

Sigma(9) = 13, tau(9) = 3 and phi(9) = 6, hence sigma(9)/tau(9) = 13/3 and sigma(9)/phi(9) = 13/6, 9 is a term.

Maple

with(numtheory): filter:= q -> (sigma(q) mod phi(q) <> 0) and (sigma(q) mod tau(q) <> 0) : select(filter, [$1..200]);

Mathematica

Select[Range[200], ! Or @@ Divisible[DivisorSigma[1, #], {DivisorSigma[0, #], EulerPhi[#]}] &] (* Amiram Eldar, Mar 08 2021 *)

Prog

(PARI) isok(m) = my(s=sigma(m)); (s % numdiv(m)) && (s % eulerphi(m)); \\ Michel Marcus, Mar 08 2021

Crossrefs

Cf. A000005 (tau), A000010 (phi), A000203 (sigma).

Cf. A020492, A003601.

Cf. A342103, A342104, A342105.

Sequence in context: A312829 A078542 A124982 * A251606 A073042 A094349

Adjacent sequences: A342103 A342104 A342105 * A342107 A342108 A342109

Keyword

nonn

Author

Bernard Schott, Mar 08 2021

Status

approved