A101181 Least positive integer that can be represented as sum of a semiprime and a square in exactly n ways.

1, 4, 13, 10, 26, 50, 58, 74, 146, 159, 218, 302, 290, 458, 515, 647, 650, 794, 962, 986, 1178, 1403, 1322, 1418, 1658, 1898, 1802, 2126, 1970, 2210, 3062, 2930, 3143, 3263, 3482, 3527, 4142, 4667, 4010, 4562, 5123, 4955, 5018, 6242, 5330, 6695, 7178, 7103

Offset

0,2

Links

Donovan Johnson, Table of n, a(n) for n = 0..1000

Formula

a(n) = min(i such that i = A001358(j) + A000290(k) in n ways).

Example

a(0) = 1 because 1 is the smallest positive integer that cannot be represented as sum of a semiprime and a square (since 4 is the smallest semiprime).
a(1) = 4 = 4 + 0; a(2) = 13 = 4 + 9 = 9 + 4; a(3) = 10 = 6 + 4
= 9 + 1 = 10 + 0.

Prog

(PARI) mx=4345802; v=vector(mx); sp=vector(856467); c=0; for(i=4, mx, if(bigomega(i)==2, c++; sp[c]=i)); for(i=0, 2084, sq=i^2; for(j=1, c, s=sq+sp[j]; if(s<=mx, v[s]++, next(2)))); n=vector(1049); for(i=4, mx, if(v[i]>0, if(n[v[i]]==0, n[v[i]]=i))); for(i=1, 1000, write("b101181.txt", i " " n[i])) /* Donovan Johnson, Feb 04 2013 */

Crossrefs

Cf. A000290, A001358, A100570.

Sequence in context: A356799 A144290 A360390 * A160249 A173800 A175174

Adjacent sequences: A101178 A101179 A101180 * A101182 A101183 A101184

Keyword

easy,nonn

Author

Jonathan Vos Post and Ray Chandler, Dec 14 2004

Status

approved