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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

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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", "))