A396541 a(1) = 1; for n > 1, a(n) is the smallest number > 7^(n-1) with exactly n divisors.

1, 11, 121, 346, 14641, 16819, 1771561, 823555, 5769604, 40353904, 25937424601, 1977326752, 3138428376721, 96889011273, 678279074929, 4747561509954, 45949729863572161, 232630513987844, 5559917313492231481, 11398895185373264, 79792288330682944, 558545864083401728

Offset

1,2

Comments

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\ | | | | | | | |

\ tau() = n | 1 | 2 | 3 | 4 | 5 | 6 | 7 |

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in \ | | | | | | | |

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[ 1..2^(n-1)]| 2^0| 2^1| 2^2| 6.. 2^3| 2^4| 12.. 2^5| 2^6 | A005179..A000079

[2^(n-1)+1..3^(n-1)]| 3^0| 3^1| 3^2| 10.. 3^3| 3^4| 44.. 3^5| 3^6 | A396139..A000244

[3^(n-1)+1..5^(n-1)]| 5^0| 5^1| 5^2| 33.. 5^3| 5^4| 244.. 5^5| 5^6 | A396206..A000351

[5^(n-1)+1..7^(n-1)]| 7^0| 7^1| 7^2|129.. 7^3| 7^4| 3141.. 7^5| 7^6 | ..A000420

[7^(n-1)+1..11^(n-1)]|11^0|11^1|11^2|346..11^3|11^4|16819..11^5|11^6 | a(n) ..A001020

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Links

Table of n, a(n) for n=1..22.

Formula

a(p) = 11^(p-1) for p prime. - Daniel Suteu, Jun 09 2026

Example

a(2) = 11 because it is the smallest number > 7^(2-1) with exactly 2 divisors;
a(3) = 121 because it is the smallest number > 7^(3-1) with exactly 3 divisors;
a(4) = 346 because it is the smallest number > 7^(4-1) with exactly 4 divisors.

Prog

(Magma) [1] cat [Min([k: k in [7^(n-1)+1..11^(n-1)] | #Divisors(k) eq n]): n in [2..7]];
(PARI) a(n) = if(n<=1, return(1)); if(isprime(n), return(11^(n-1))); for(k=7^(n-1)+1, oo, if(numdiv(k) == n, return(k))); \\ Daniel Suteu, Jun 09 2026

Crossrefs

Cf. A000005, A001020.

Cf. A005179, A396139, A396206.

Sequence in context: A240942 A216131 A338784 * A223392 A262468 A221964

Adjacent sequences: A396538 A396539 A396540 * A396543 A396544 A396545

Keyword

nonn,less

Author

Juri-Stepan Gerasimov, May 28 2026

Extensions

a(15)-a(22) from Daniel Suteu, Jun 09 2026

Status

approved