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

1,1

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

Prog

(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(d<n && sigma(d)>2*d, return(0))); (1));
is_A378742(n) = (is_A091191(n) && (A378664(n)==6));

Crossrefs

Cf. A378664.

After the initial term, a subsequence of A378738.

Subsequence of A008588 and of A091191.

Sequence in context: A304833 A363591 A223234 * A289223 A296914 A285580

Adjacent sequences: A378739 A378740 A378741 * A378743 A378744 A378745

Keyword

nonn

Author

Antti Karttunen, Dec 07 2024

Status

approved