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A285100 Numbers k for which A065642(k) = A285109(k).

%I A285100 #19 Mar 23 2025 18:26:03
%S A285100 1,2,3,4,5,6,7,8,9,10,11,13,14,15,16,17,19,20,21,22,23,25,26,27,28,29,
%T A285100 30,31,32,33,34,35,37,38,39,41,42,43,44,46,47,49,51,52,53,55,57,58,59,
%U A285100 61,62,64,65,66,67,68,69,70,71,73,74,76,77,78,79,81,82,83,85,86,87,88,89,91,92,93,94,95,97,99,101
%N A285100 Numbers k for which A065642(k) = A285109(k).
%H A285100 Antti Karttunen, <a href="/A285100/b285100.txt">Table of n, a(n) for n = 1..10000</a>
%o A285100 (PARI)
%o A285100 A020639(n) = if(1==n,n,vecmin(factor(n)[, 1]));
%o A285100 A007947(n) = factorback(factorint(n)[, 1]); \\ From _Andrew Lelechenko_, May 09 2014
%o A285100 A065642(n) = { my(r=A007947(n)); if(1==n,n,n = n+r; while(A007947(n) <> r, n = n+r); n); };
%o A285100 isA285100(n) = (A065642(n) == n*A020639(n));
%o A285100 n=0; k=1; while(k <= 10000, n=n+1; if(isA285100(n),write("b285100.txt", k, " ", n);k=k+1));
%o A285100 (Scheme)
%o A285100 ;; With _Antti Karttunen_'s IntSeq-library.
%o A285100 (define A285100 (MATCHING-POS 1 1 (lambda (n) (= (A065642 n) (A285109 n)))))
%o A285100 (Python)
%o A285100 from operator import mul
%o A285100 from sympy import primefactors
%o A285100 from functools import reduce
%o A285100 def a007947(n): return 1 if n<2 else reduce(mul, primefactors(n))
%o A285100 def a020639(n): return 1 if n==1 else primefactors(n)[0]
%o A285100 def a065642(n):
%o A285100     if n==1: return 1
%o A285100     r=a007947(n)
%o A285100     n += r
%o A285100     while a007947(n)!=r:
%o A285100         n+=r
%o A285100     return n
%o A285100 print([n for n in range(1, 102) if a065642(n) == n*a020639(n)]) # _Indranil Ghosh_, May 24 2017
%Y A285100 Complement: A284342.
%Y A285100 Positions of ones in A285337.
%Y A285100 Subsequences: A000961, A005117.
%Y A285100 Cf. A065642, A285109.
%K A285100 nonn
%O A285100 1,2
%A A285100 _Antti Karttunen_, Apr 19 2017