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

Author

Ilya Gutkovskiy, Dec 19 2022

Keywords

• nonn
• more

Links

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

Crossrefs

Cf. A000330, A001222, A359192.

Programs

PARI

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

Extensions

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