

A071142


Numbers n such that sum of distinct primes dividing n is divisible by the largest prime dividing n. Also n has exactly 3 distinct prime factors and n is squarefree.


3



30, 70, 286, 646, 1798, 3526, 7198, 10366, 20806, 23326, 38086, 44998, 64798, 73726, 78406, 103966, 115198, 145798, 159046, 194686, 242206, 352798, 373246, 426886, 544966, 649798, 719998, 763846, 824326, 871198, 1312198, 1351366, 1371166, 1472326, 1555846
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OFFSET

1,1


LINKS

Donovan Johnson, Table of n, a(n) for n = 1..1000


FORMULA

A008472(n)/A006530(n) is integer; a(n) = 2*A037074(n), n = 2pq, where p and q = p+2 are twin prime pairs.


EXAMPLE

n = 2*p*q = 2p(p+2); sum = 2+p+q = 2+p+p+2, where p and q are twin prime pairs.


MATHEMATICA

ffi[x_] := Flatten[FactorInteger[x]] lf[x_] := Length[FactorInteger[x]] ba[x_] := Table[Part[ffi[x], 2*w1], {w, 1, lf[x]}] sb[x_] := Apply[Plus, ba[x]] ma[x_] := Part[Reverse[Flatten[FactorInteger[x]]], 2] amo[x_] := Abs[MoebiusMu[x]] Do[s=sb[n]/ma[n]; If[IntegerQ[s]&&Equal[lf[n], 3]&& !Equal[amo[n], 0], Print[{n, ba[n]}]], {n, 2, 1000000}]


CROSSREFS

Cf. A008472, A006530, A000961, A025475, A037074, A071139A071147.
Sequence in context: A301900 A071141 A071312 * A218327 A259753 A308137
Adjacent sequences: A071139 A071140 A071141 * A071143 A071144 A071145


KEYWORD

nonn


AUTHOR

Labos Elemer, May 13 2002


STATUS

approved



