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A162651 Numbers which can be expressed as the product of 3 positive integers in arithmetic progression. 1
1, 6, 8, 15, 24, 27, 28, 45, 48, 60, 64, 66, 80, 91, 105, 120, 125, 153, 162, 168, 190, 192, 210, 216, 224, 231, 276, 280, 288, 312, 315, 325, 336, 343, 360, 378, 384, 405, 435, 440, 480, 496, 504, 510, 512, 528, 561, 585, 624, 627, 630, 640, 648, 693, 703, 720 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Numbers of the form i*(i+j)*(i+2j), where i > 0 and j >= 0.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

1 = 1*1*1, 6 = 1*2*3, 8 = 2*2*2, 15 = 1*3*5, 24 = 2*3*4.

120 = 1*8*15 = 2*6*10 = 4*5*6.

MAPLE

N:= 1000: # for all terms <= N

S:= {}:

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

  S:= S union {seq(i*(i+j)*(i+2*j), j=0..floor((sqrt(i^4 + 8*i*N)-3*i^2)/(4*i)))}

od:

A:= sort(convert(S, list)); # Robert Israel, Feb 05 2020

PROG

(PARI) al(n)={local(v, inc, prd);

v=vector(n); inc=[0]; prd=[1];

for(k=1, n,

v[k]=vecmin(prd);

if(v[k]==prd[ #prd], inc=concat(inc, [0]); prd=concat(prd, [(#inc)^3]));

for(j=1, #prd, if(prd[j]==v[k], inc[j]++; prd[j]=j*(j+inc[j])*(j+2*inc[j]))));

v}

CROSSREFS

Cf. A000578, A007531, A000384, A033996, A011199.

Sequence in context: A315925 A315926 A063534 * A275321 A022320 A318387

Adjacent sequences:  A162648 A162649 A162650 * A162652 A162653 A162654

KEYWORD

nonn

AUTHOR

Franklin T. Adams-Watters, Jul 08 2009

STATUS

approved

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Last modified January 24 12:11 EST 2022. Contains 350536 sequences. (Running on oeis4.)