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

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

Cf. A227754.

Sequence in context: A174456 A306474 A250053 * A096595 A324257 A083359

Adjacent sequences: A227752 A227753 A227754 * A227756 A227757 A227758

Keyword

nonn,easy

Author

Giovanni Resta, Jul 26 2013

Status

approved