A379466 - OEIS

%I #11 Jan 29 2025 09:26:43

%S 4104,13832,32832,39312,64232,65728,110656,110808,165464,171288,

%T 262656,314496,320264,373464,513000,513856,525824,805688,885248,

%U 886464,955016,994688,1009736,1016496,1061424,1075032,1092728,1323712,1331064,1370304,1407672,1609272,1728216,1729000,1734264,1774656,2101248

%N Taxicab numbers that are abundant.

%C 5835375 is the smallest odd term in the sequence.

%C If a is a taxicab number and b is abundant, then a * b^3 is a term.  In particular, the sequence is infinite. - _Robert Israel_, Jan 29 2025

%H Robert Israel, <a href="/A379466/b379466.txt">Table of n, a(n) for n = 1..500</a>

%e 4104=2^3*3^3*19 is a term because it is a Taxicab number (2^3+16^3=9^3+15^3) and it is smaller than the sum of its proper divisors (1+2+3+4+6+8+9+12+18+19+24+27+36+38+54+ 57+72+76+108+114+152+171+216+228+342+456+513+684+1026+1368+2052=7896). 13832=2^3*7*13*19 is a term because it is a Taxicab number (13832=2^3+24^3=18^3+20^3) and it is smaller than the sum of its proper divisors (1+2+4+7+8+13+14+19+26+28+38+ 52+56+76+91+104+133+152+182+247+266+364+494+532+728+988+1064+1729+1976+3458+6916=19768).

%p N:= 10^7: # for terms <= N

%p V:= Vector(N, datatype=integer[4]):

%p for i from 0 to floor(N^(1/3)) do

%p   for j from max(1,i) do

%p     k:= i^3 + j^3;

%p     if k > N then break fi;

%p     V[k]:= V[k]+1

%p od od:

%p select(k -> V[k] >= 2 and numtheory:-sigma(k) > 2*k, [$1..N]); # _Robert Israel_, Jan 29 2025

%t Select[Import["https://oeis.org/A001235/b001235.txt", "Table"][[;; , 2]], # < 3*10^6 && DivisorSigma[-1, #] > 2 &] (* _Amiram Eldar_, Dec 23 2024 *)

%Y Intersection of A001235 and A005101.

%K nonn

%O 1,1

%A _Massimo Kofler_, Dec 23 2024