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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.
2
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 A135178 A278583
KEYWORD
nonn
AUTHOR
Vladeta Jovovic, Oct 07 2001
EXTENSIONS
Title clarified by Sean A. Irvine, Jul 15 2023
STATUS
approved