A263107 Number of ordered pairs (k, m) with k > 0 and m > 0 such that n = pi(k^2/2) + pi(3*m^2/2), where pi(x) denotes the number of primes not exceeding x.
1, 1, 1, 2, 2, 1, 3, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 1, 4, 5, 1, 6, 3, 4, 5, 2, 4, 5, 2, 5, 5, 3, 4, 5, 4, 6, 2, 4, 4, 6, 3, 4, 5, 2, 6, 8, 1, 5, 6, 2, 4, 7, 3, 6, 5, 2, 6, 7, 1, 4, 7, 3, 6, 5, 3, 7, 4, 5, 5, 6, 5, 5, 4, 2, 6, 10, 3, 4, 6, 5, 3, 6, 5, 7, 3
Offset: 1
Keywords
Examples
a(1) = 1 since 1 = 1 + 0 = pi(2^2/2) + pi(3*1^2/2). a(2) = 1 since 2 = 2 + 0 = pi(3^2/2) + pi(3*1^2/2). a(3) = 1 since 3 = 0 + 3 = pi(1^2/2) + pi(3*2^2/2). a(6) = 1 since 6 = 0 + 6 = pi(1^2/2) + pi(3*3^2/2). a(19) = 1 since 19 = 7 + 12 = pi(6^2/2) + pi(3*5^2/2). a(22) = 1 since 22 = 1 + 21 = pi(2^2/2) + pi(3*7^2/2). a(48) = 1 since 48 = 1 + 47 = pi(2^2/2) + pi(3*12^2/2). a(60) = 1 since 60 = 25 + 35 = pi(14^2/2) + pi(3*10^2/2). a(396) = 1 since 396 = 334 + 62 = pi(67^2/2) + pi(3*14^2/2). a(1076) = 1 since 1076 = 47 + 1029 = pi(21^2/2) + pi(3*74^2/2). a(3033) = 1 since 3033 = 7 + 3026 = pi(6^2/2) + pi(3*136^2/2). a(3889) = 1 since 3889 = 1808 + 2081 = pi(176^2/2) + pi(3*110^2/2). a(4741) = 1 since 4741 = 4699 + 42 = pi(301^2/2) + pi(3*11^2/2). a(6804) = 1 since 6804 = 6047 + 757 = pi(346^2/2) + pi(3*62^2/2). a(7919) = 1 since 7919 = 4049 + 3870 = pi(277^2/2) + pi(3*156^2/2). a(9604) = 1 since 9604 = 4754 + 4850 = pi(303^2/2) + pi(3*177^2/2). a(16938) = 1 since 16938 = 2223 + 14715 = pi(198^2/2) + pi(3*327^2/2). a(19169) = 1 since 19169 = 6510 + 12659 = pi(361^2/2) + pi(3*301^2/2). a(32533) = 1 since 32533 = 1768 + 30765 = pi(174^2/2) + pi(3*490^2/2). a(59903) = 1 since 59903 = 59210 + 693 = pi(1213^2/2) + pi(3*59^2/2). a(100407) = 1 since 100407 = 7554 + 92853 = pi(392^2/2) + pi(3*894^2/2).
Links
- Zhi-Wei Sun, Table of n, a(n) for n = 1..10000
Programs
-
Mathematica
s[n_]:=s[n]=PrimePi[3n^2/2] t[n_]:=t[n]=PrimePi[n^2/2] Do[r=0;Do[If[s[k]>n, Goto[bb]];Do[If[t[j]>n-s[k],Goto[aa]];If[t[j]==n-s[k],r=r+1];Continue,{j, 1, n-s[k]+1}];Label[aa];Continue, {k, 1, n}];Label[bb];Print[n," ",r]; Continue,{n,1,100}]
Comments