A285100 - OEIS

%I #13 May 07 2021 08:33:16

%S 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 30,31,32,33,34,35,37,38,39,41,42,43,44,46,47,49,51,52,53,55,57,58,59,

%U 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 Numbers n for which A065642(n) = A285109(n).

%H Antti Karttunen, <a href="/A285100/b285100.txt">Table of n, a(n) for n = 1..10000</a>

%o (PARI)

%o A020639(n) = if(1==n,n,vecmin(factor(n)[, 1]));

%o A007947(n) = factorback(factorint(n)[, 1]); \\ From _Andrew Lelechenko_, May 09 2014

%o A065642(n) = { my(r=A007947(n)); if(1==n,n,n = n+r; while(A007947(n) <> r, n = n+r); n); };

%o isA285100(n) = (A065642(n) == n*A020639(n));

%o n=0; k=1; while(k <= 10000, n=n+1; if(isA285100(n),write("b285100.txt", k, " ", n);k=k+1));

%o (Scheme, with _Antti Karttunen_'s IntSeq-library)

%o (define A285100 (MATCHING-POS 1 1 (lambda (n) (= (A065642 n) (A285109 n)))))

%o (Python)

%o from operator import mul

%o from sympy import primefactors

%o from functools import reduce

%o def a007947(n): return 1 if n<2 else reduce(mul, primefactors(n))

%o def a020639(n): return 1 if n==1 else primefactors(n)[0]

%o def a065642(n):

%o     if n==1: return 1

%o     r=a007947(n)

%o     n += r

%o     while a007947(n)!=r:

%o         n+=r

%o     return n

%o print([n for n in range(1, 102) if a065642(n) == n*a020639(n)]) # _Indranil Ghosh_, May 24 2017

%Y Complement: A284342.

%Y Positions of ones in A285337.

%Y Subsequences: A000961, A005117.

%Y Cf. A065642, A285109.

%K nonn

%O 1,2

%A _Antti Karttunen_, Apr 19 2017