A331082 Smallest number having exactly n divisors ending with 3 or 7.

3, 21, 63, 189, 567, 693, 3969, 2079, 5733, 6237, 413343, 9009, 74529, 43659, 51597, 27027, 1750329, 63063, 26040609, 81081, 464373, 670761, 219667417263, 153153, 2528253, 819819, 693693, 729729, 160137547184727, 567567, 6036849, 459459, 37614213, 19253619

Offset: 1

Author

Andrew Howroyd, Jan 08 2020

Keywords

• nonn
• base

Comments

A term cannot be a multiple of either 2 or 5 since removing these factors does not alter the number of divisors ending with 3 or 7.

All terms must be in A331029.

Examples

			a(1) = 3: divisors of 3 are 1, 3*. (* marks divisors ending in 3 or 7.)
a(2) = 21: divisors of 21 are 1, 3*, 7*, 21.
a(3) = 63: divisors of 63 are 1, 3*, 7*, 9, 21, 63*.
a(4) = 189: divisors of 189 are 1, 3*, 7*, 9, 21, 27*, 63*, 189.
		

Crossrefs

Cf. A085645, A331029.

Programs

PARI

a(n)={forstep(k=1, oo, 2, if(sumdiv(k, d, abs(d%10-5)==2) == n, return(k)))}

PARI

\\ faster program: needs lista331029 defined in A331029.
a(n)={my(lim=1); while(1, lim*=10; my(S=lista331029(lim)); for(i=1, #S, my(k=S[i]); if(sumdiv(k, d, abs(d%10-5)==2)==n, return(k))))}

Python

from sympy import divisors
def count37(iterable): return sum(i%10 in [3, 7] for i in iterable)
def a(n):
  m = 2
  while count37(divisors(m)) != n: m += 1
  return m
print([a(n) for n in range(1, 17)]) # Michael S. Branicky, Mar 21 2021