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.

12, 66, 102, 174, 186, 222, 246, 258, 282, 318, 354, 366, 402, 426, 438, 474, 498, 534, 582, 606, 618, 642, 654, 678, 762, 786, 822, 834, 894, 906, 942, 978, 1002, 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

Offset: 1

Author

Antti Karttunen, Dec 07 2024

Keywords

• nonn

Comments

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.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A378664.

After the initial term, a subsequence of A378738.

Subsequence of A008588 and of A091191.

Programs

PARI

A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A341612(n) = ((sigma(n)<=(2*n))&&((2*n)<A003961(n)));
A378664(n) = { fordiv(n,d,if(A341612(n/d), return(n/d))); (1); };
is_A091191(n) = if(sigma(n)<=2*n, 0, fordiv(n,d,if(d2*d, return(0))); (1));
is_A378742(n) = (is_A091191(n) && (A378664(n)==6));