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A285639 a(n) = n*A117366(n)/spf(n), where A117366(n) is the smallest prime larger than all prime factors of n, and spf is the smallest prime factor of n (or 1 if n = 1).

%I A285639 #70 Jan 23 2018 17:32:53
%S A285639 2,3,5,6,7,15,11,12,15,35,13,30,17,77,35,24,19,45,23,70,77,143,29,60,
%T A285639 35,221,45,154,31,105,37,48,143,323,77,90,41,437,221,140,43,231,47,
%U A285639 286,105,667,53,120,77,175,323,442,59,135,143,308,437,899,61,210,67,1147
%N A285639 a(n) = n*A117366(n)/spf(n), where A117366(n) is the smallest prime larger than all prime factors of n, and spf is the smallest prime factor of n (or 1 if n = 1).
%C A285639 The smallest prime factor of n is removed, and a prime factor larger than all others is added. This is somewhat in the spirit of A003961 where each of the prime factors is increased to the next larger prime. Therefore a(n) = A003961(n) when n is a prime or a product of consecutive primes.
%C A285639 Leaves invariant A073485, i.e., for all n in A073485, a(n) is again in A073485. More precisely, a(A098012(m,n)) = A098012(m,n+1). - _M. F. Hasler_, May 03 2017
%H A285639 Ivan Neretin, <a href="/A285639/b285639.txt">Table of n, a(n) for n = 1..10000</a>
%e A285639 a(1) = nextprime(1) = 2.
%e A285639 a(2) = 2 / 2 * nextprime(2) = 3.
%e A285639 a(3) = 3 / 3 * nextprime(3) = 5, and in the same way, a(prime(k))=prime(k+1).
%e A285639 a(4) = 4 / 2 * nextprime(2) = 2*3 = 6.
%e A285639 a(6) = 6 / 2 * nextprime(3) = 3*5 = 15.
%t A285639 Table[d = FactorInteger[n]; n*NextPrime[d[[-1, 1]]]/d[[1, 1]], {n, 62}] (* _Ivan Neretin_, Jan 23 2018 *)
%o A285639 (PARI) a(n,f=factor(n)[,1])={f||f=[1];n\f[1]*nextprime(f[#f]+1)}
%Y A285639 Cf. A020639, A003961, A006530, A117366, A151800.
%K A285639 nonn
%O A285639 1,1
%A A285639 _M. F. Hasler_, Apr 30 2017