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

1,1

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

Mathematica

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

Prog

(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

Crossrefs

Intersection of A000037 and A045572.

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

Sequence in context: A102213 A276283 A377232 * A310192 A138152 A004139

Adjacent sequences: A158939 A158940 A158941 * A158943 A158944 A158945

Keyword

nonn,easy

Author

Eric Desbiaux, Mar 31 2009

Extensions

New name from Charles R Greathouse IV, Sep 05 2013

Status

approved