A076551 -id:A076551 - cp's OEIS frontend

A359017 a(n) is the index of the smallest triangular number with exactly n distinct prime factors.

1, 2, 3, 11, 20, 84, 455, 1364, 10659, 58695, 254540, 728364, 13516580, 133595384, 812646120, 5327923964, 68971338435, 838101203939, 7588384207404, 69322940121435, 490005293940084

Offset: 0

Ilya Gutkovskiy, Dec 12 2022

Eric Weisstein's World of Mathematics, Distinct Prime Factors
Eric Weisstein's World of Mathematics, Triangular Number

Cf. A000217, A001221, A076550, A076551.

a(n) = my(k=1); while(omega(k*(k+1)/2) != n, k++); k; \\ Michel Marcus, Feb 26 2023

a(19)-a(20) from Michael S. Branicky, Feb 25 2023

A375658 The smallest triangular number that begins a run of at least n consecutive triangular numbers with the same number of distinct prime factors.

Original entry on oeis.org

1, 6, 6, 6, 6, 6, 6, 6, 103327500, 1977230170, 214596675756, 2796022463625, 32291440570378, 32291440570378, 549091407981061, 4680505857819681, 96914999755056255, 96914999755056255

Offset: 1

Shyam Sunder Gupta, Aug 23 2024

			a(8) = 6 because 6 is the smallest triangular number that begins a run of 8 consecutive triangular numbers (6, 10, 15, 21, 28, 36, 45, 55) with the same number of distinct prime factors, i.e. 2.
a(9) = 103327500 because 103327500 is the smallest triangular number that begins a run of 9 consecutive triangular numbers (103327500, 103341876, 103356253, 103370631, 103385010, 103399390,  103413771, 103428153, 103442536) with the same number of distinct prime factors, i.e. 5.

Cf. A000217, A069903, A076551.

Cf. A375657.

cp's OEIS Frontend

A359017 a(n) is the index of the smallest triangular number with exactly n distinct prime factors.

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A375658 The smallest triangular number that begins a run of at least n consecutive triangular numbers with the same number of distinct prime factors.

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