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%I #29 Jun 06 2020 03:19:09
%S 1,6,15,28,30,33,40,42,51,66,69,84,91,95,102,105,117,120,135,138,140,
%T 141,145,159,165,182,186,190,210,213,224,231,234,255,270,273,280,282,
%U 285,287,290,295,308,318,321,330,345,357,364,395,420,426,435,440,445,455
%N Numbers k divisible by the largest prime factor of the sum of divisors of k; a(1) = 1.
%C Pomerance (1973) proved that all the harmonic numbers (A001599) are in this sequence.
%C If m is a product of distinct Mersenne primes (A046528), m > 1 and 3 | m, then 2*m is a term.
%C If p is a term of A005105 then, 6*p is a term for p > 3, and 3*p is a term if p is not a Mersenne prime (A000668).
%H Amiram Eldar, <a href="/A333646/b333646.txt">Table of n, a(n) for n = 1..10000</a>
%H Carl Pomerance, On a Problem of Ore: Harmonic Numbers, unpublished manuscript, 1973; abstract *709-A5, Notices of the American Mathematical Society, Vol. 20, 1973, page A-648, <a href="https://www.ams.org/journals/notices/197311/197311FullIssue.pdf">entire volume</a>.
%F Numbers k such that A071190(k) | k.
%e 15 is a term since sigma(15) = 24, 3 is the largest prime factor of 24, and 15 is divisible by 3.
%t Select[Range[500], Divisible[#, FactorInteger[DivisorSigma[1, #]][[-1, 1]]] &]
%Y A001599 and A105402 are subsequences.
%Y Cf. A000203, A000668, A005105, A006530, A046528, A071190.
%K nonn
%O 1,2
%A _Amiram Eldar_, Jun 05 2020
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