cp's OEIS Frontend

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.

%I A064518 #20 Mar 26 2025 17:34:15
%S A064518 1,12,36,144,432,1296,1728,5184,15552,20736,46656,62208,186624,248832,
%T A064518 559872,746496,1679616,2239488,2985984,6718464,8957952,20155392,
%U A064518 26873856,60466176,35831808,80621568,107495424,241864704,322486272
%N 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.
%C A064518 It is not difficult to show that these numbers have the form a(n) = 3^i*4^j with j <= i <= 2j.
%H A064518 Sean A. Irvine, <a href="/A064518/b064518.txt">Table of n, a(n) for n = 1..1000</a> (terms 1..50 from Harry J. Smith)
%F A064518 a(n) = 3^A064514(n) * 4^A064515(n). - _Chai Wah Wu_, Mar 26 2025
%o A064518 (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
%Y A064518 Every term is also a term of A064476.
%Y A064518 Cf. A064514, A064515.
%K A064518 nonn
%O A064518 1,2
%A A064518 _Vladeta Jovovic_, Oct 07 2001
%E A064518 Title clarified by _Sean A. Irvine_, Jul 15 2023