A064518 For an integer n with prime factorization p_1*p_2*p_3* ... *p_m let n* = (p_1+1)*(p_2+1)*(p_3+1)* ... *(p_m+1); sequence gives n* such that n* is divisible by n, ordered by increasing value of n.

1, 12, 36, 144, 432, 1296, 1728, 5184, 15552, 20736, 46656, 62208, 186624, 248832, 559872, 746496, 1679616, 2239488, 2985984, 6718464, 8957952, 20155392, 26873856, 60466176, 35831808, 80621568, 107495424, 241864704, 322486272

Offset

1,2

Comments

It is not difficult to show that these numbers have the form a(n) = 3^i*4^j with j <= i <= 2j.

Links

Sean A. Irvine, Table of n, a(n) for n = 1..1000 (terms 1..50 from Harry J. Smith)

Prog

(PARI) ns(n)= { local(f, p=1); f=factor(n); for(i=1, matsize(f)[1], p*=(1 + f[i, 1])^f[i, 2]); return(p) } { n=0; for (m=1, 10^9, s=ns(m); if (s%m == 0, write("b064518.txt", n++, " ", s); if (n==50, break)) ) } \\ Harry J. Smith, Sep 17 2009

Crossrefs

Every term is also a term of A064476.

Sequence in context: A073403 A191817 A270840 * A238923 A380033 A135178

Adjacent sequences: A064515 A064516 A064517 * A064519 A064520 A064521

Keyword

nonn

Author

Vladeta Jovovic, Oct 07 2001

Extensions

Title clarified by Sean A. Irvine, Jul 15 2023

Status

approved