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 A074837 Numbers n such that the penultimate 3 divisors of n sum to n. 2

%I

%S 6,18,42,54,66,78,102,114,126,138,162,174,186,198,222,234,246,258,282,

%T 294,306,318,342,354,366,378,402,414,426,438,462,474,486,498,522,534,

%U 546,558,582,594,606,618,642,654,666,678,702,714,726,738,762,774,786

%N Numbers n such that the penultimate 3 divisors of n sum to n.

%C It seems that only numbers that are 6 mod 12 are present except for multiples of 30.

%H Harvey P. Dale, <a href="/A074837/b074837.txt">Table of n, a(n) for n = 1..1000</a>

%e 18 has the divisors 1,2,3,6,9,18. The penultimate 3 are 3,6,9, which sum to 18.

%t Select[Range[1000],Length[Divisors[ # ]]>3 && Sum[Divisors[ # ][[ -i]],{i,2,4}]==# &] (* _Stefan Steinerberger_, Aug 01 2007 *)

%t p3dQ[n_]:=Module[{d=Divisors[n]},Length[d]>3&&Total[Take[Most[d],-3]] == n]; Select[Range[800],p3dQ] (* _Harvey P. Dale_, Dec 06 2012 *)

%o (PARI) for (n=1,300,dn=divisors(n); dnl=length(dn); if (dnl>3,if (n==dn[dnl-1]+dn[dnl-2]+dn[dnl-3],print(n))))

%K nonn

%O 1,1

%A _Jon Perry_, Sep 09 2002

%E More terms from _Stefan Steinerberger_, Aug 01 2007

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Last modified June 14 15:19 EDT 2021. Contains 345025 sequences. (Running on oeis4.)