

A123651


1+n^2+n^3+n^5+n^7+n^11+n^13+n^17.


2



8, 141485, 130914100, 17251189841, 764209065776, 16940083223773, 232729381165100, 2252358161564225, 16679754951397336, 100010100010101101, 505481836542757988, 2218718842990269265, 8650720586711446400
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OFFSET

1,1


COMMENTS

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^15n^13+2n^11n^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.


LINKS

Table of n, a(n) for n=1..13.


FORMULA

a(n) = 1 + n^2 + n^3 + n^5 + n^7 + n^11 + n^13 + n^17 = 100010100010101101 (base n) = +/ (n^2+1)*(n^15n^13+2n^11n^9+n^7+n^3+1)


MATHEMATICA

Table[Total[n^Prime[Range[7]]]+1, {n, 20}] (* Harvey P. Dale, Aug 22 2012 *)


CROSSREFS

Cf. A002522, A098547, A123111, A123113, A123650, A123652.
Sequence in context: A036535 A048565 A123276 * A210812 A223939 A013846
Adjacent sequences: A123648 A123649 A123650 * A123652 A123653 A123654


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, Oct 04 2006


STATUS

approved



