A359192 -id:A359192 - cp's OEIS frontend

A359193 a(n) is the index of the smallest square pyramidal number with exactly n prime factors (counted with multiplicity).

1, 2, 3, 4, 7, 15, 24, 31, 63, 80, 175, 255, 511, 1023, 512, 6912, 2047, 6655, 14336, 16384, 32767, 90112, 131071, 180224, 483327, 1114112, 1638400, 2097151, 1048575, 16777216, 8388607, 33357824, 16777215, 92274687, 67108864

Offset: 0

Ilya Gutkovskiy, Dec 19 2022

Eric Weisstein's World of Mathematics, Prime Factor
Eric Weisstein's World of Mathematics, Square Pyramidal Number

Cf. A000330, A001222, A359192.

sp(n) = n*(n+1)*(2*n+1)/6; \\ A000330
a(n) = my(k=1); while (bigomega(sp(k)) != n, k++); k; \\ Michel Marcus, Dec 20 2022

a(26)-a(34) from Daniel Suteu, Dec 29 2022

A359229 a(n) is the smallest square pyramidal number with exactly n distinct prime factors.

Original entry on oeis.org

1, 5, 14, 30, 1785, 6930, 149226, 3573570, 139223370, 3708968340, 62366724420, 2279301054030, 1348519628145690, 27928822496705130, 1558931949520935990, 430616881400429491950, 161887663616926971163440

Offset: 0

Ilya Gutkovskiy, Dec 22 2022

			a(4) = 1785, because 1785 is a square pyramidal number with 4 distinct prime factors {3, 5, 7, 17} and this is the smallest such number.

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

Cf. A000330, A001221, A156329, A359192, A359230.

a(16) from Jon E. Schoenfield, Dec 22 2022

cp's OEIS Frontend

A359193 a(n) is the index of the smallest square pyramidal number with exactly n prime factors (counted with multiplicity).

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