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A227755 The average of prime factors of n and n+1 is the same. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 28 06:00 EST 2021. Contains 340490 sequences. (Running on oeis4.)