cp's OEIS Frontend

A378742 Primitively abundant numbers k for which A378664(k) = 6, where A378664 is the greatest divisor d of n such that sigma(d) <= 2*d < A003961(d), or 1 if no such divisor exists.

%I A378742 #10 Jul 23 2025 16:06:48
%S A378742 12,66,102,174,186,222,246,258,282,318,354,366,402,426,438,474,498,
%T A378742 534,582,606,618,642,654,678,762,786,822,834,894,906,942,978,1002,
%U A378742 1038,1074,1086,1146,1158,1182,1194,1266,1338,1362,1374,1398,1434,1446,1506,1542,1578,1614,1626,1662,1686,1698,1758,1842,1866
%N A378742 Primitively abundant numbers k for which A378664(k) = 6, where A378664 is the greatest divisor d of n such that sigma(d) <= 2*d < A003961(d), or 1 if no such divisor exists.
%C A378742 Apparently all the terms are of the form 6*p, where p is any prime except one of the 3, 5, 7, 13, 19, 23.
%H A378742 Antti Karttunen, <a href="/A378742/b378742.txt">Table of n, a(n) for n = 1..20000</a>
%o A378742 (PARI)
%o A378742 A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A378742 A341612(n) = ((sigma(n)<=(2*n))&&((2*n)<A003961(n)));
%o A378742 A378664(n) = { fordiv(n,d,if(A341612(n/d), return(n/d))); (1); };
%o A378742 is_A091191(n) = if(sigma(n)<=2*n, 0, fordiv(n,d,if(d<n && sigma(d)>2*d, return(0))); (1));
%o A378742 is_A378742(n) = (is_A091191(n) && (A378664(n)==6));
%Y A378742 Cf. A378664.
%Y A378742 After the initial term, a subsequence of A378738.
%Y A378742 Subsequence of A008588 and of A091191.
%K A378742 nonn
%O A378742 1,1
%A A378742 _Antti Karttunen_, Dec 07 2024