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%I #12 Dec 18 2016 13:50:29
%S 24,225504,944108,10869375,11506989,12792675,20962395,25457760,
%T 79509528,89002914,89460294,146767704,161064864,180173147,219487320,
%U 235762488,252508509,419785344,434887029,453160511,487179000,545112792,813133607
%N Numbers n such that sopf(n) divides sopf(n+1) and sopf(n+1) divides sopf(n+2).
%C The sum of the distinct primes dividing n (without repetition) is sometimes called sopf(n).
%C (A008472(a(n)+1) mod A008472(a(n)) = 0) and (A008472(a(n)+2) mod A008472(a(n)+1) = 0). [From _Reinhard Zumkeller_, Mar 12 2010]
%D M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 844.
%D T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 38.
%D J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 225504, p. 264, Ellipses, Paris 2008.
%H Donovan Johnson, <a href="/A173172/b173172.txt">Table of n, a(n) for n = 1..100</a>
%H W. Sierpinski, <a href="http://matwbn.icm.edu.pl/ksiazki/mon/mon42/mon4204.pdf">Number Of Divisors And Their Sum</a>
%H M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, <a href="http://apps.nrbook.com/abramowitz_and_stegun/index.html">Applied Math. Series 55, Tenth Printing, 1972 </a>[alternative scanned copy].
%e sopf(24) = 5, sopf(25) = 5, sopf(26) = 15; and 5 divides 5, 5 and divides 15.
%e sopf(225504) = 34, sopf(225505) = 408, sopf(225506) = 2448; and 34 divides 408, and 408 divides 2448.
%p with(numtheory): for n from 2 to 100000000 do : t1 := ifactors(n)[2] : t2 := sum(t1[i][1], i=1..nops(t1)) : tt1 :=ifactors(n+1)[2] :tt2 := sum(tt1[i][1], i=1..nops(tt1)): ttt1:=ifactors(n+2)[2] : ttt2 := sum(ttt1[i][1], i=1..nops(ttt1)): a:= tt2/t2 ; aa:=floor(a) ;b := ttt2/tt2:bb:=floor(b): if a=aa and b=bb then print (n): else fi: od:
%K nonn
%O 1,1
%A _Michel Lagneau_, Feb 11 2010
%E a(12)-a(23) from _Donovan Johnson_, Feb 13 2010
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