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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.
0
24574158, 29146163, 156385858, 173105316, 246414308, 404413338, 553659041, 556221794, 745644336, 760923063, 789864069, 794287963, 893806805, 983628183, 1033093563, 1134287383, 1138839886, 1418521141, 1559578963, 1702800491, 1750142480, 2080676083, 2117324180
OFFSET
1,1
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
EXAMPLE
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.
PROG
(Magma) [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)];
(PARI) is(n)=for(k=9*n+1, 9*n+8, if(issquarefree(k), return(0))); 1 \\ Charles R Greathouse IV, Jun 02 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
a(3)-a(8) from Charles R Greathouse IV, Jun 02 2015
a(9)-a(23) from Charles R Greathouse IV, Jun 03 2015
STATUS
approved

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Last modified September 19 21:59 EDT 2024. Contains 376015 sequences. (Running on oeis4.)