1,1

This polynomial, A(21,n), is surprisingly reducible over Z, and thus prime-free. A(21,n) = 21st row of semiprime power sum array A(k,n) = 1 + SUM[i=1..k]n^semiprime(i) = 1 + SUM[i=1..k]n^A001358(i). If we deem semiprime(0) = 1, the array is A(k,n) = SUM[i=0..k]n^A001358(i). A(1,n) = first row of semiprime power sum array = 1+n^4 = A002523(n) = 10001(base n). Primes in the first row are A091940. A(2,n) = 2nd row of semiprime power sum array = A123656. A(3,n) = 3rd row of semiprime power sum array is A123657. A(4,n) = 4th row of semiprime power sum array is A123658. A(5,n) = 5th row of semiprime power sum array is A123659. A(6,n) = 6th row of semiprime power sum array is A123659. A(n,n) = A123177 Main diagonal of semiprime power sum array.

a(n) = 1+n^4+n^6+n^9+n^10+n^14+n^15+n^21+n^22+n^25+n^26+ n^33+n^34+n^35+n^38+n^39+n^46+n^49+n^51+n^55+n^57+n^58 = +/- (n+1)*(n^57+n^54-n^53+n^52-n^51+2*n^50-2*n^49+3*n^48-3*n^47+3*n^46 -2*n^45+2*n^44-2*n^43+2*n^42-2*n^41+2*n^40-2*n^39+3*n^38-2*n^37+2*n^36 -2*n^35+3*n^34-2*n^33+3*n^32-3*n^31+3*n^30-3*n^29+3*n^28-3*n^27+3*n^26 -2*n^25+3*n^24-3*n^23+3*n^22-2*n^21+3*n^20-3*n^19+3*n^18-3*n^17+3*n^16 -3*n^15+4*n^14-3*n^13+3*n^12-3*n^11+3*n^10-2*n^9+3*n^8-3*n^7+3*n^6-2*n^5+2*n^4-n^3+n^2-n+1) = 11010001010010000001100111000000110011000001100011001010001 (base n).

Cf. A001358, A002523, A091940, A123177, A123656-A123665.

Sequence in context: A104784 A013902 A056667 this_sequence A119566 A092993 A114784

Adjacent sequences: A123662 A123663 A123664 this_sequence A123666 A123667 A123668

easy,nonn

Jonathan Vos Post (jvospost2(AT)yahoo.com), Oct 04 2006