A279815 Numbers n such that the average of the squares of the numbers less than n that do not divide n is an integer.

3, 4, 7, 13, 16, 19, 20, 31, 37, 43, 61, 67, 73, 79, 97, 103, 109, 127, 139, 151, 157, 163, 181, 188, 193, 199, 211, 223, 229, 241, 271, 277, 283, 307, 313, 331, 337, 349, 367, 373, 379, 397, 409, 421, 433, 439, 457, 463, 487, 499, 523, 541, 547, 571, 577, 601, 607, 613, 619, 631, 643, 661, 673, 691, 709, 727, 733, 739, 751, 757, 769, 787

Offset

1,1

Comments

Numbers n such that A049820(n) divides A276984(n).

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

7 is in the sequence because 7 has 2 divisors {1,7} therefore 5 non-divisors {2,3,4,5,6}, 2^2 + 3^2 + 4^2 + 5^2 + 6^2 = 90 and 5 divides 90.

Mathematica

Select[Range[800], Mod[#1 (#1 + 1) ((2 #1 + 1)/6) - DivisorSigma[2, #1], #1 - DivisorSigma[0, #1]] == 0 & ]

Prog

(PARI) is(n)=my(f=factor(n)); n>2 && ((2*n^3+3*n^2+n)/6-sigma(f, 2))%(n-numdiv(f))==0 \\ Charles R Greathouse IV, Dec 19 2016

Crossrefs

Cf. A020486, A049820, A140826, A276984.

Sequence in context: A049930 A102938 A076784 * A088764 A093124 A055664

Adjacent sequences: A279812 A279813 A279814 * A279816 A279817 A279818

Keyword

nonn,easy

Author

Ilya Gutkovskiy, Dec 19 2016

Status

approved