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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). 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 16 17:39 EDT 2021. Contains 348042 sequences. (Running on oeis4.)