# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a119616 Showing 1-1 of 1 %I A119616 #32 Dec 15 2023 06:19:37 %S A119616 0,2,3,14,5,47,7,70,39,97,11,287,13,163,158,310,17,533,19,609,262,343, %T A119616 23,1375,155,457,390,1043,29,1942,31,1302,542,733,502,3185,37,895,718, %U A119616 2945,41,3358,43,2247,1859,1267,47,5983,399,2697,1142,3017,53,5150,1006 %N A119616 Second elementary symmetric function of divisors of n. %C A119616 a(p)=p if p is prime and records are A002093 (highly abundant numbers). - _Robert G. Wilson v_, Jun 07 2006 %H A119616 Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe) %F A119616 a(n) = Sum_{u|n, v|n, u (l-> add(add(l[i]*l[j], i=1..j-1), j=2..nops(l))) %p A119616 (sort([numtheory[divisors](n)[]])): %p A119616 seq(a(n), n=1..80); # _Alois P. Heinz_, Jun 25 2014 %t A119616 f[n_] := Block[{d = Divisors@n}, Sum[ d[[u]]*d[[v]], {v, 2, Length@d}, {u, v - 1}]]; Array[f, 55] (* _Robert G. Wilson v_ *) %o A119616 (PARI) a(n)=my(d=divisors(n));sum(i=1,#d-1,sum(j=i+1,#d,d[i]*d[j])) \\ _Charles R Greathouse IV_, Mar 05 2013 %o A119616 (PARI) a(n)=(sigma(n)^2-sigma(n,2))/2 \\ _Charles R Greathouse IV_, Mar 05 2013 %Y A119616 Cf. A002093, A000203, A001157, A002117, A067692. %Y A119616 Column k=2 of A224381. %K A119616 nonn,easy %O A119616 1,2 %A A119616 _N. J. A. Sloane_, based on email from Neven Juric (neven.juric(AT)apis-it.hr), Jun 07 2006 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE