A070007 Arithmetic mean of distinct primes dividing n is a square number.

15, 42, 45, 65, 75, 77, 84, 87, 126, 135, 141, 168, 225, 247, 252, 258, 261, 285, 294, 301, 325, 335, 336, 357, 375, 378, 405, 410, 423, 429, 481, 504, 516, 539, 588, 589, 591, 618, 671, 672, 675, 717, 756, 767, 774, 783, 785, 820, 845, 847, 855, 882, 986

Offset: 1

Author

Labos Elemer, Apr 11 2002

Keywords

• nonn

Comments

Subset of A078174. [R. J. Mathar, Sep 20 2008]

Examples

			n=1972=2*17*29: mean=(2+17+29)/3=48/3=16, a square.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A070005, A070006, A001414, A008472.

Programs

Mathematica

Select[Range[2, 1000], IntegerQ@ Sqrt[Total[First /@ FactorInteger@ #]/PrimeNu@ #] &] (* Michael De Vlieger, Mar 28 2015 *)

PARI

lista(nn) = {for (n=2, nn, f = factor(n); if ((#f~ != 1) && (type(q=sum(k=1, #f~, f[k,1])/#f~) == "t_INT") && issquare(q), print1(n, ", ")););} \\ Michel Marcus, Mar 28 2015