cp's OEIS Frontend

A123651 a(n) = 1 + n^2 + n^3 + n^5 + n^7 + n^11 + n^13 + n^17.

%I A123651 #12 Sep 08 2022 08:45:28
%S A123651 8,141485,130914100,17251189841,764209065776,16940083223773,
%T A123651 232729381165100,2252358161564225,16679754951397336,
%U A123651 100010100010101101,505481836542757988,2218718842990269265,8650720586711446400
%N A123651 a(n) = 1 + n^2 + n^3 + n^5 + n^7 + n^11 + n^13 + n^17.
%C A123651 7th row, A(7,n), of the infinite array A(k,n) = 1 + Sum_{i=1..k} n^prime(i). If we deem prime(0) = 1, the array is A(k,n) = Sum_{i=0..k} n^prime(i). The first row is A002522 = 1 + n^2. The second row is A098547 = 1 + n^2 + n^3. The 3rd row, A(3,n), is A123650. The 4th row, A(4,n), is A123111 1 + n^2 + n^3 + n^5 + n^7. 10101101 (base n). A(n,n) is A123113 Main diagonal of prime power sum array. The current sequence, A(7,n), can never be prime, because of the polynomial factorization a(n) = 1 + n^2 + n^3 + n^5 + n^7 + n^11 + n^13 + n^17 = +/- (n^2+1)*(n^15 -n^13 +2n^11 -n^9 +n^7 +n^3 +1). It can be semiprime, as with a(2) and with a(10) = 100010100010101101 = 101 * 990199010001001 and a(14). We similarly have polynomial factorization for A123652 = A(13,n) = 1 +n^2 +n^3 +n^5 +...+ n^41.
%H A123651 G. C. Greubel, <a href="/A123651/b123651.txt">Table of n, a(n) for n = 1..1000</a>
%F A123651 a(n) = 1 + n^2 + n^3 + n^5 + n^7 + n^11 + n^13 + n^17 = 100010100010101101 (base n) = +/- (n^2+1)*(n^15-n^13+2n^11-n^9+n^7+n^3+1).
%t A123651 Table[Total[n^Prime[Range[7]]]+1,{n,20}] (* _Harvey P. Dale_, Aug 22 2012 *)
%o A123651 (PARI) for(n=1,25, print1(1 + n^2 + n^3 + n^5 + n^7 + n^11 + n^13 + n^17, ", ")) \\ _G. C. Greubel_, Oct 17 2017
%o A123651 (Magma) [1 + n^2 + n^3 + n^5 + n^7 + n^11 + n^13 + n^17: n in [1..25]]; // _G. C. Greubel_, Oct 17 2017
%Y A123651 Cf. A002522, A098547, A123111, A123113, A123650, A123652.
%K A123651 easy,nonn
%O A123651 1,1
%A A123651 _Jonathan Vos Post_, Oct 04 2006