A156238 Smallest heptagonal number with n distinct prime factors.

7, 18, 286, 3010, 32890, 769230, 3333330, 159189030, 16015883940, 477463360374, 21643407275490, 1148540321999070, 18489352726664820, 4561561662153109614, 71000485538666794110, 14440652550858108745170, 927869754030522488795610

Offset: 1

Author

Donovan Johnson, Feb 07 2009

Keywords

• nonn

Comments

a(18) <= 150849873309136386205130310. - Donovan Johnson, Feb 15 2012

Examples

			a(9) = 16015883940 = 2^2*3^2*5*7*17*19*23*29*59. 16015883940 is the smallest heptagonal number with 9 distinct prime factors.
		

Links

• Eric Weisstein's World of Mathematics, Heptagonal Numbers.

Crossrefs

Cf. A000566, A076551, A156236, A156237, A156239.

Programs

Python

from sympy import primefactors
def A000566(n): return n*(5*n-3)//2
def a(n):
    k = 1
    while len(primefactors(A000566(k))) != n: k += 1
    return A000566(k)
print([a(n) for n in range(1, 9)]) # Michael S. Branicky, Jul 18 2021

Python

# faster version using heptagonal structure
from sympy import primefactors
def A000566(n): return n*(5*n-3)//2
def A000566_distinct_factors(n):
    pf1 = primefactors(n)
    pf2 = primefactors(5*n-3)
    combined = set(pf1) | set(pf2)
    return len(combined) if n%4 == 0 or (5*n-3)%4 == 0 else len(combined)-1
def a(n):
    k = 1
    while A000566_distinct_factors(k) != n: k += 1
    return A000566(k)
print([a(n) for n in range(1, 10)]) # Michael S. Branicky, Jul 18 2021

Extensions

a(17) from Donovan Johnson, Jul 02 2011