A258211 -id:A258211 - cp's OEIS frontend

A258332 Numbers n such that 4n + 1, 4n + 2 and 4n + 3 are not squarefree.

211, 420, 722, 906, 2731, 3687, 3962, 4351, 4985, 5505, 5656, 5818, 6162, 6443, 7337, 7562, 7731, 8293, 9175, 9312, 9681, 9861, 10118, 11343, 11918, 11931, 11956, 12093, 12372, 13646, 13756, 13862, 14280, 14618, 14712, 14981, 15306, 15716, 15743, 15961, 16512, 17162, 17237

Offset: 1

Juri-Stepan Gerasimov, May 26 2015

			211 is in this sequence because 4 * 211 + 1 = 845 = 5 * 13^2, 4 * 211 + 2 = 846 = 2 * 3^2 * 47 and 4 * 211 + 3 = 847 = 7 * 11^2.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A188296, A258211.

[n: n in [1..20000] | not IsSquarefree(4*n+1) and  not IsSquarefree(4*n+2) and not IsSquarefree(4*n+3)];

remove(t->ormap(numtheory:-issqrfree,[4*t+1,4*t+2,4*t+3]), [$1..2*10^4]); # Robert Israel, Apr 03 2018

Select[Range[1000], Union[{MoebiusMu[4# + 1], MoebiusMu[4# + 2], MoebiusMu[4# + 3]}] == {0} &] (* Alonso del Arte, May 26 2015 *)

isok(n) = !issquarefree(4*n+1) && !issquarefree(4*n+2) && !issquarefree(4*n+3); \\ Michel Marcus, Apr 04 2018

A256013 Numbers n such that none of 9n + 1, 9n + 2, 9n + 3, 9n + 4, 9n + 5, 9n + 6, 9n + 7 and 9n + 8 are squarefree.

Original entry on oeis.org

24574158, 29146163, 156385858, 173105316, 246414308, 404413338, 553659041, 556221794, 745644336, 760923063, 789864069, 794287963, 893806805, 983628183, 1033093563, 1134287383, 1138839886, 1418521141, 1559578963, 1702800491, 1750142480, 2080676083, 2117324180

Offset: 1

Juri-Stepan Gerasimov, May 31 2015

nonn

Two of 9n+1..9n+8 are multiples of 4, so concentrate on the other six. The probability that any k of these six are all squarefree is P(k) := Product {p prime > 3} (p^2-k)/p^2. By inclusion-exclusion, the probability that none of the six are squarefree is 1 - 6P(1) + 15P(2) - 20P(3) + 15P(4) - 6P(5) + P(6), or roughly one in 92600000. - Michael R Peake, Apr 04 2017

			24574158 is in this sequence because
9 * 24574158 + 1 = 221167423 = 230143 * 31^2,
9 * 24674158 + 2 = 221167424 = 3455741 * 2^6,
9 * 24674158 + 3 = 221167425 = 128213 * 23 * 5^3,
9 * 24674158 + 4 = 221167426 = 80777 * 2 * 37^2,
9 * 24674158 + 5 = 221167427 = 45127 * 29 * 13^2,
9 * 24674158 + 6 = 221167428 = 18430619 * 3 * 2^2,
9 * 24674158 + 7 = 221167429 = 33937 * 19 * 7^3,
9 * 24674158 + 8 = 221167430 = 3889 * 47 * 5 * 2 * 11^2.

Cf. A013929, A258211, A258332.

[n: n in [1..25000000] | not IsSquarefree(9*n+1) and not IsSquarefree(9*n+2) and not IsSquarefree(9*n+3) and not IsSquarefree(9*n+4) and not IsSquarefree(9*n+5) and not IsSquarefree(9*n+6) and not IsSquarefree(9*n+7) and not IsSquarefree(9*n+8)];

is(n)=for(k=9*n+1,9*n+8,if(issquarefree(k),return(0))); 1 \\ Charles R Greathouse IV, Jun 02 2015

a(3)-a(8) from Charles R Greathouse IV, Jun 02 2015

a(9)-a(23) from Charles R Greathouse IV, Jun 03 2015

cp's OEIS Frontend

A258332 Numbers n such that 4n + 1, 4n + 2 and 4n + 3 are not squarefree.

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