A158942 Nonsquares coprime to 10.

3, 7, 11, 13, 17, 19, 21, 23, 27, 29, 31, 33, 37, 39, 41, 43, 47, 51, 53, 57, 59, 61, 63, 67, 69, 71, 73, 77, 79, 83, 87, 89, 91, 93, 97, 99, 101, 103, 107, 109, 111, 113, 117, 119, 123, 127, 129, 131, 133, 137, 139, 141, 143, 147, 149, 151, 153, 157, 159, 161, 163

Offset: 1

Author

Eric Desbiaux, Mar 31 2009

Keywords

• nonn
• easy

Comments

Odd primes + odd nonprime integers that have an odd numbers of proper divisors A082686, are the result of a suppression of integers satisfying: 2n (A005843); n^2 (A000290); n^2+n (A002378). Of these, we can suppress the multiples of 5 (A008587).

Decimal expansion of 1/10^(n^2+n) + 1/10^(n^2) + 1/10^(5*n) + 1/10^(2*n) gives a 0 for these integers.

2n + n(n+1) + n^2 = 2n^2 + 3n = A014106.

2n^2 + 3n + 5n = 2n^2 + 8n = 2n(n+4) = A067728 8(8+n) is a perfect square.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A000037 and A045572.

Cf. A082868, A002378, A000290, A005843, A008587, A014106, A067728.

Programs

Mathematica

Select[Range@ 163, ! IntegerQ@ Sqrt@ # && CoprimeQ[#, 10] &] (* Michael De Vlieger, Dec 11 2015 *)

PARI

isok(n) = (n % 2) && (n % 5) && (isprime(n) || (numdiv(n) % 2 == 0)); \\ Michel Marcus, Aug 27 2013

PARI

is(n)=gcd(n,10)==1 && !issquare(n) \\ Charles R Greathouse IV, Sep 05 2013

Extensions

New name from Charles R Greathouse IV, Sep 05 2013