A386972 Numbers that are the product of a semiprime and the square of another semiprime.
96, 144, 160, 224, 240, 324, 336, 352, 360, 400, 416, 486, 504, 528, 540, 544, 560, 600, 608, 624, 736, 756, 784, 792, 810, 816, 880, 900, 912, 928, 936, 992, 1040, 1104, 1134, 1176, 1184, 1188, 1215, 1224, 1232, 1260, 1312, 1350, 1360, 1368, 1376, 1392, 1400, 1404, 1456, 1488, 1500
Offset: 1
Keywords
Examples
96 = 6 * 4^2; 144 = 9 * 4^2 or 4 * 6^2.
Links
- David A. Corneth, First 1000000 terms colorcoded by prime signature
Programs
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Maple
M:= 2000: # for terms <= M P:= select(isprime, [2,seq(i,i=3..M/8,2)]): nP:= nops(P): S:= {}: for i1 from 1 to nP do p1:= P[i1]; if p1^2*4^2 > M then break fi; for i2 from i1 to nP do p2:= P[i2]; if p1*p2*4^2 > M then break fi; for i3 from 1 to nP do p3:= P[i3]; if p1*p2*p3^4 > M then break fi; for i4 from i3 to nP do p4:= P[i4]; v:= p1*p2*(p3*p4)^2; if v > M then break fi; if p1*p2 = p3*p4 then next fi; S:= S union {v} od od od od: sort(convert(S,list)); # Robert Israel, Aug 11 2025 -
Mathematica
Select[Range@ 1500, MemberQ[{{1,5}, {2,4}, {1,1,4}, {1,2,3}, {2,2,2}, {1,1,2,2}}, Sort[ Last /@ FactorInteger[#]]] &] (* Giovanni Resta, Aug 12 2025 *) -
PARI
is(n) = {my(f = factor(n), b = bigomega(f)); if(b != 6, return(0)); f = vecsort(f[,2]~); #setminus(Set([f]), Set([[1, 5], [2, 4], [1, 1, 4], [1, 2, 3], [2, 2, 2], [1, 1, 2, 2]])) == 0} \\ David A. Corneth, Aug 12 2025
Comments