A333916 -id:A333916 - cp's OEIS frontend

A333915 Number of ways to represent n as a pyramidal number.

1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 3, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2

Offset: 4

Ilya Gutkovskiy, Apr 09 2020

nonn

Frequency of n in the array A261720 of pyramidal numbers.

			a(10) = 2 because 10 is the third tetrahedral (or triangular pyramidal) number and also the second 9-gonal pyramidal number.
a(30) = 3 because 30 is the fourth square pyramidal number, the third octagonal pyramidal number and also the second 29-gonal pyramidal number.

Eric Weisstein's World of Mathematics, Pyramidal Number
Index to sequences related to pyramidal numbers

Cf. A080851, A129654, A177025, A261720, A333916.

A333932 a(n) is the least integer that is 4-dimensional pyramidal in exactly n ways.

Original entry on oeis.org

5, 15, 35, 140, 1820, 11375, 820820, 19019000, 10790015600, 1568726956160, 7278234628665, 7271181889157550

Offset: 1

Ilya Gutkovskiy, Apr 10 2020

a(n) has exactly n representations as an 4-dimensional pyramidal number P(m, k) = binomial(k + 2, 3)*(k*(m - 2) - m + 6) / 4, with m > 2, k > 1.

			a(3) = 35 because 35 is the least integer which is 4-dimensional pyramidal in 3 ways (35 = P(3, 4) = P(7, 3) = P(33, 2)).

Index to sequences related to pyramidal numbers

Cf. A063778, A080852, A261721, A333916.

a(9) from Giovanni Resta, Apr 11 2020

a(9) corrected and a(10)-a(12) from Bert Dobbelaere, Apr 14 2020

cp's OEIS Frontend

A333915 Number of ways to represent n as a pyramidal number.

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