# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/

Search: id:a351551
Showing 1-1 of 1

%I A351551 #32 Jul 09 2022 18:31:43
%S A351551 1,2,10,34,106,120,216,260,340,408,440,580,672,696,820,1060,1272,1666,
%T A351551 1780,1940,2136,2340,2464,3320,3576,3960,4280,4536,5280,5380,5860,
%U A351551 6456,6960,7520,8746,8840,9120,9632,10040,10776,12528,12640,13464,14560,16180,16660,17400,17620,19040,19416,19992,21320,22176,22968
%N A351551 Numbers k such that the largest unitary divisor of sigma(k) that is coprime with A003961(k) is also a unitary divisor of k.
%C A351551 Numbers k for which A351546(k) is a unitary divisor of k.
%C A351551 The condition guarantees that A351555(k) = 0, therefore this is a subsequence of A351554.
%C A351551 The condition is also a necessary condition for A349745, therefore it is a subsequence of this sequence.
%C A351551 All six known 3-perfect numbers (A005820) are included in this sequence.
%C A351551 All 65 known 5-multiperfects (A046060) are included in this sequence.
%C A351551 Not all multiperfects (A007691) are present (only 587 of the first 1600 are), but all 23 known terms of A323653 are terms, while none of the (even) terms of A046061 or A336702 are.
%H A351551 Antti Karttunen, <a href="/A351551/b351551.txt">Table of n, a(n) for n = 1..20223</a>
%H A351551 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A351551 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%e A351551 For n = 672 = 2^5 * 3^1 * 7^1, and the largest unitary divisor of the sigma(672) [= 2^5 * 3^2 * 7^1] coprime with A003961(672) [= 13365 = 3^5 * 5^1 * 11^1] is 2^5 * 7^1 = 224, therefore A351546(672) is a unitary divisor of 672, and 672 is included in this sequence.
%o A351551 (PARI)
%o A351551 A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A351551 A351546(n) = { my(f=factor(sigma(n)),u=A003961(n)); prod(k=1,#f~,f[k,1]^((0!=(u%f[k,1]))*f[k,2])); };
%o A351551 isA351551(n) =  { my(u=A351546(n)); (!(n%u) && 1==gcd(u,n/u)); };
%Y A351551 Cf. A000203, A000396, A003961, A007691, A046061, A065997, A336702, A351546, A351555, A353633 (characteristic function).
%Y A351551 Subsequence of A351552 and of A351554.
%Y A351551 Cf. A349745, A351550 (subsequences), A005820, A046060, A323653 (very likely subsequences).
%K A351551 nonn
%O A351551 1,2
%A A351551 _Antti Karttunen_, Feb 16 2022

# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE