A227755 - OEIS

A227755

The average of prime factors of n and n+1 is the same.

735, 2172, 3484, 6324, 6747, 6867, 7424, 7865, 14012, 14640, 35321, 39284, 42172, 47724, 57075, 60155, 63664, 89975, 104923, 105412, 113283, 114204, 149144, 151959, 153924, 155708, 176860, 189780, 221705, 230124, 244035, 250995, 327700, 349811, 351075, 357752

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OFFSET

1,1

COMMENTS

Up to 10^13 there is only one triple of consecutive numbers, starting at 18140055498, which have the same average of prime factors.

LINKS

Giovanni Resta, Table of n, a(n) for n = 1..1000

EXAMPLE

735 is in the sequence since 735 = 3*5*7^2, 736 = 2^5*23 and (3+5+7+7)/4 = (2+2+2+2+2+23)/6.

MATHEMATICA

avepa[n_] := Block[{f = FactorInteger[n]}, Total[Times @@@ f]/Total[Last /@ f]]; Select[Range[2, 10^5], avepa[#] == avepa[#+1] &]

CROSSREFS