A132315 Sum of the non-fourth powers less than or equal to n.

0, 2, 5, 9, 14, 20, 27, 35, 44, 54, 65, 77, 90, 104, 119, 119, 136, 154, 173, 193, 214, 236, 259, 283, 308, 334, 361, 389, 418, 448, 479, 511, 544, 578, 613, 649, 686, 724, 763, 803, 844, 886, 929, 973, 1018, 1064, 1111, 1159, 1208, 1258, 1309, 1361, 1414, 1468

Offset

1,2

Links

Table of n, a(n) for n=1..54.

Formula

Let r = floor(n^(1/4)). Then a(n) = n(n+1)/2 - (r^5/5+r^4/2+r^3/3-r/30).

Example

Let n=16.
The sum of the non-quartic numbers <= 16 is 2+3+4+5+6+7+8+9+10+11+12+13+14+15 = 119, the 16th entry in the sequence.

Prog

(PARI) g4(n)=for(x=1, n, r=floor(x^(1/4)); sum4=r^5/5+r^4/2+r^3/3-r/30; sn=x*(x+1)/2; print1(sn-sum4", "))

Crossrefs

Sequence in context: A275586 A333449 A075543 * A079509 A132336 A272370

Adjacent sequences: A132312 A132313 A132314 * A132316 A132317 A132318

Keyword

nonn

Author

Cino Hilliard, Nov 07 2007

Status

approved