login
A349774
Numbers that start a run of four consecutive triangular numbers with four prime factors (counted with multiplicity).
0
161596, 222778, 366796, 962578, 1611910, 2480878, 3301165, 4290985, 13320541, 23588146, 29272726, 43743981, 50818321, 68041945, 79512355, 100614205, 143981965, 161757091, 172896310, 194626585, 200710630, 275338311, 282161890, 352331785, 410712130, 457062495, 457092730
OFFSET
1,1
EXAMPLE
a(1) = 161596 because 161596 is the smallest number in the first set of four consecutive triangular numbers with four prime factors (counted with multiplicity), i.e., (161596 = 2*2*71*569, 162165 = 3*5*19*569, 162735 = 3*5*19*571, 163306 = 2*11*13*571).
MATHEMATICA
t[n_] := n*(n + 1)/2; q[n_] := PrimeOmega[n] == 4; Select[Partition[t /@ Range[35000], 4, 1], AllTrue[#, q] &][[;; , 1]] (* Amiram Eldar, Nov 29 2021 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Shyam Sunder Gupta, Nov 29 2021
STATUS
approved