cp's OEIS Frontend

A374218 After the initial 1, numbers k such that A347381 obtains its minimum value at k, of all the divisors d of k larger than one, where A347381 is the distance from n to the nearest common ancestor of n and sigma(n) in the Doudna-tree (A005940).

%I A374218 #19 Jul 12 2024 21:16:31
%S A374218 1,2,6,15,28,77,189,496,899,945,1271,1403,2125,3127,3139,6375,8128,
%T A374218 8383,9261,13843,15247,15631,30240,32760,45151,46305,47263,54053,
%U A374218 54653,58339,63767,65473,73813,79567,89951,92783,94957,97969,133907,142859,155011,161257,189209,211621,249001,293323,333961,360883,368063
%N A374218 After the initial 1, numbers k such that A347381 obtains its minimum value at k, of all the divisors d of k larger than one, where A347381 is the distance from n to the nearest common ancestor of n and sigma(n) in the Doudna-tree (A005940).
%C A374218 Not all terms of A347383 are included here. The first missing ones are 226967, 925101, 961193, 4566661, 6031163, 6064439, 11234875.
%H A374218 Antti Karttunen, <a href="/A374218/b374218.txt">Table of n, a(n) for n = 1..85</a>
%H A374218 <a href="/index/O#opnseqs">Index entries for sequences where odd perfect numbers must occur, if they exist at all</a>
%F A374218 {k | A347381(k) = A374204(k)}.
%F A374218 {k | A347381(k) <= A374214(k)}.
%e A374218 189 has divisors 3, 7, 9, 21, 27, 63, 189 larger than 1. A347381 applied to them gives 1, 3, 2, 4, 3, 3, 1, so the largest divisor 189 gets minimal value 1 (which also occurs at the smallest prime divisor 3), thus 189 is included in this sequence.
%e A374218 496 has divisors 2, 4, 8, 16, 31, 62, 124, 248, 496 larger than 1. A347381 applied to them gives 0, 1, 2, 3, 10, 10, 9, 12, 0, so the largest divisor 496 gets minimal value 0 (which also occurs at the smallest prime divisor 2), thus 496 is included in this sequence.
%e A374218 1271 has divisors 31, 41, 1271 larger than 1. A347381 applied to them gives 10, 10, 9, of which minimal value 9 occurs at the largest divisor (1271 itself), thus 1271 is included in this sequence.
%o A374218 (PARI) isA374218(n) = if(n>2 && isprime(n), 0, my(w=A347381(n)); fordiv(n, d, if(d>1 && d<n && A347381(d)<w, return(0))); (1));
%Y A374218 Cf. A347381, A347383, A374204, A374214.
%Y A374218 Indices of nonpositive terms in A374215.
%Y A374218 Cf. A336702, A374219 (subsequences).
%K A374218 nonn
%O A374218 1,2
%A A374218 _Antti Karttunen_, Jul 07 2024