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

1,1

Comments

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

Links

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A070005, A070006, A001414, A008472.

Sequence in context: A056698 A371108 A371050 * A380217 A325041 A154267

Adjacent sequences: A070004 A070005 A070006 * A070008 A070009 A070010

Keyword

nonn

Author

Labos Elemer, Apr 11 2002

Status

approved