A338784 a(n) is the smallest number with exactly n divisors such that all its divisors end with the same digit (which is necessarily 1).

1, 11, 121, 341, 14641, 3751, 1771561, 13981, 116281, 453871, 25937424601, 153791, 3138428376721, 54918391, 14070001, 852841, 45949729863572161, 4767521, 5559917313492231481, 18608711, 1702470121, 804060162631, 81402749386839761113321, 9381251, 13521270961, 97291279678351, 195468361

Offset

1,2

Comments

As 1 is a divisor for each number, all the divisors must end with 1.

Links

David A. Corneth, Table of n, a(n) for n = 1..966

Project Euler, Problem 474: Last digits of divisors.

Formula

If n is prime p, then a(p) = 11^(p-1) = A001020(p-1).

For k>=1, a(2^k) = {Product_m=1..k} A030430(m) = A092609(k).

Example

121 is the smallest number whose 3 divisors (1, 11, 121) end with 1, hence a(3) = 121.
3751 is the smallest number whose 6 divisors (1, 11, 31, 121, 341, 3751) end with 1, hence a(6) = 121.
a(18) = 4767521 = 11^2 * 31^2 * 41 as it has 18 divisors all of which end in 1. - David A. Corneth, Nov 09 2020

Prog

(PARI) a(n) = {my(pr); if(n==1, return(1)); if(isprime(n), return(11^(n-1))); forstep(i = 1, oo, 10, f = factor(i); if(numdiv(f) == n, pr = 1; for(j = 1, #f~, if(f[j, 1]%10 != 1, pr = 0; next(2) ) ) ); if(pr, return(i)); ) } \\ David A. Corneth, Nov 09 2020

Crossrefs

Cf. A001020, A030430, A092609, A330348.

Subsequence of A004615.

Sequence in context: A223223 A240942 A216131 * A223392 A262468 A221964

Adjacent sequences: A338781 A338782 A338783 * A338785 A338786 A338787

Keyword

nonn,base

Author

Bernard Schott, Nov 09 2020

Extensions

Data corrected by David A. Corneth, Nov 09 2020

Status

approved