A268513 Numbers n such that bigomega(n) = bigomega(n*(n+1)+41).

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 43, 47, 49, 53, 59, 61, 65, 67, 71, 73, 79, 82, 83, 87, 91, 97, 101, 103, 107, 113, 121, 122, 123, 131, 137, 139, 143, 149, 151, 155, 157, 159, 161, 167, 178, 179, 181, 185, 187, 191, 193, 197, 199

Offset: 1

Author

Zak Seidov, Feb 06 2016

Keywords

• nonn

Examples

			Let eu(x) = x*(x + 1) + 41 and n-AP= n-almost prime, then:
both 2 and eu(2)=47 are primes,
both 49=7*7 and eu(49)=47*53 are semiprimes,
both 574=2*7*41 and eu(574)=41*83*97 are 3-AP,
both 3484=2^2*13*67 and eu(3484)=12141781=41*43*71*97 are 4-AP,
both 54224=2^4*3389 and eu(2940296441)=43^2*61*131*199 are 5-AP,
both 506022=2*3*11^2*17*41 and eu(506022)=41*43^2*71*113*421 are 6-AP,
both 7375900=2^2*5^2*7*41*257 and eu(7375900)=41*47*53*71^2*251*421 are 7-AP,
both 151072290=2*3^4*5*41*4549 and eu(151072290)=41*47*61*83*113^2*167*1097 are 8-AP.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A001222, A202018.

Programs

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

Mathematica

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

PARI

isok(n) = bigomega(n) == bigomega(n^2+n+41); \\ Michel Marcus, Feb 07 2016