A307589 Numbers m such that 1 < gcd(m, 35) < m and m does not divide 35^e for e >= 0.

10, 14, 15, 20, 21, 28, 30, 40, 42, 45, 50, 55, 56, 60, 63, 65, 70, 75, 77, 80, 84, 85, 90, 91, 95, 98, 100, 105, 110, 112, 115, 119, 120, 126, 130, 133, 135, 140, 145, 147, 150, 154, 155, 160, 161, 165, 168, 170, 180, 182, 185, 189, 190, 195, 196, 200, 203, 205

Offset

1,1

Comments

Complement of the union of A003595 and A235933.

Analogous to A081062 and A105115 for terms 1 and 2 of A120944. This sequence applies to A120944(6) = 35.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Formula

a(n) = 35n/11 + O(log^2 n). - Charles R Greathouse IV, Sep 07 2022

Example

10 is in the sequence since gcd(10, 35) = 5 and 10 does not divide 35^e with integer e >= 0.
2 is not in the sequence since 2 is coprime to 35.
7 is not in the sequence since 7 | 35.
25 is not in the sequence since 25 | 35^2.

Mathematica

With[{nn = 205, k = 35}, Select[Range@ nn, And[1 < GCD[#, k] < #, PowerMod[k, Floor@ Log2@ nn, #] != 0] &]]

Prog

(PARI) is(n)=gcd(n, 35)>1 && n/5^valuation(n, 5)/7^valuation(n, 7)>1 \\ Charles R Greathouse IV, Sep 07 2022

Crossrefs

Cf. A003595, A081062, A105115, A120944, A235933, A306999.

Sequence in context: A317590 A081062 A330136 * A209800 A119613 A154371

Adjacent sequences: A307586 A307587 A307588 * A307590 A307591 A307592

Keyword

nonn,easy

Author

Michael De Vlieger, Aug 22 2019

Status

approved