A268513 - OEIS

%I #20 Sep 08 2022 08:46:15

%S 2,3,5,7,11,13,17,19,23,29,31,37,43,47,49,53,59,61,65,67,71,73,79,82,

%T 83,87,91,97,101,103,107,113,121,122,123,131,137,139,143,149,151,155,

%U 157,159,161,167,178,179,181,185,187,191,193,197,199

%N Numbers n such that bigomega(n) = bigomega(n*(n+1)+41).

%H Zak Seidov, <a href="/A268513/b268513.txt">Table of n, a(n) for n = 1..20000</a>

%e Let eu(x) = x*(x + 1) + 41 and n-AP= n-almost prime, then:

%e both 2 and eu(2)=47 are primes,

%e both 49=7*7 and eu(49)=47*53 are semiprimes,

%e both 574=2*7*41 and eu(574)=41*83*97 are 3-AP,

%e both 3484=2^2*13*67 and eu(3484)=12141781=41*43*71*97 are 4-AP,

%e both 54224=2^4*3389 and eu(2940296441)=43^2*61*131*199 are 5-AP,

%e both 506022=2*3*11^2*17*41 and eu(506022)=41*43^2*71*113*421 are 6-AP,

%e both 7375900=2^2*5^2*7*41*257 and eu(7375900)=41*47*53*71^2*251*421 are 7-AP,

%e both 151072290=2*3^4*5*41*4549 and eu(151072290)=41*47*61*83*113^2*167*1097 are 8-AP.

%t Select[Range[100], PrimeOmega[#] == PrimeOmega[# (# + 1) + 41] &]

%o (PARI) isok(n) = bigomega(n) == bigomega(n^2+n+41); \\ _Michel Marcus_, Feb 07 2016

%o (Magma)  [n: n in [2..200] | &+[d[2]: d in Factorization(n)] eq &+[d[2]: d in Factorization(n^2+n+41)] ]; // _Vincenzo Librandi_, Feb 08 2016

%Y Cf. A001222, A202018.

%K nonn

%O 1,1

%A _Zak Seidov_, Feb 06 2016