A077351 -id:A077351 - cp's OEIS frontend

A077352 a(n) = (concatenation in ascending order of divisors of 2^n)/2^n.

1, 6, 31, 156, 7801, 390051, 19502551, 9751275501, 4875637750501, 2437818875250501, 12189094376252505001, 60945471881262525005001, 304727359406312625025005001, 1523636797031563125125025005001, 76181839851578156256251250250050001, 3809091992578907812812562512502500050001

Offset: 0

Amarnath Murthy, Nov 05 2002

			a(6) = 1248163264/64 = 19502551.

Paolo Xausa, Table of n, a(n) for n = 0..80

Cf. A000079, A034887, A059268, A077351, A069872, A077353.

a:= n-> parse(cat(2^i$i=0..n))/2^n:
seq(a(n), n=0..15);  # Alois P. Heinz, May 16 2025

A077352[n_] := FromDigits[Flatten[IntegerDigits[Divisors[#]]]]/# & [2^n];
Array[A077352, 16, 0] (* or *)
FoldList[10^IntegerLength[2^#2]*#/2 + 1 &, 1, Range[15]] (* Paolo Xausa, May 19 2025 *)

For n>=1, a(n) = (a(n-1)*2^(n-1)*10^(floor(log_10(2^n))+1)+2^n)/2^n. - Sam Alexander, Feb 27 2005

Offset corrected by Sean A. Irvine, May 16 2025

A077353 a(n) = (concatenation in ascending order of divisors of 5^n)/5^n.

Original entry on oeis.org

1, 3, 61, 12201, 2440201, 4880402001, 97608040020001, 1952160800400020001, 390432160080004000200001, 780864320160008000400002000001, 1561728640320016000800004000002000001, 31234572806400320016000080000040000020000001, 6246914561280064003200016000008000004000000200000001

Offset: 0

Amarnath Murthy, Nov 05 2002

			a(5) = 15251256253125/3125 = 4880402001.

Paolo Xausa, Table of n, a(n) for n = 0..50

Cf. A000351, A055642, A077351, A069872, A077352.

a:= n-> parse(cat(5^i$i=0..n))/5^n:
seq(a(n), n=0..12);  # Alois P. Heinz, May 16 2025

A077353[n_] := FromDigits[Flatten[IntegerDigits[Divisors[#]]]]/# & [5^n];
Array[A077353, 16, 0] (* or *)
FoldList[10^IntegerLength[5^#2]/5*# + 1 &, 1, Range[15]] (* Paolo Xausa, May 19 2025 *)

a(n) = eval(concat(apply(x->Str(x),divisors(5^n))))/5^n \\ Max Alekseyev, Dec 12 2011

a(n) = if(n==0,1,(10^#Str(5^n)/5)*a(n-1)+1) \\ Jason Yuen, Aug 21 2024

a(0) = 1, a(n) = (10^A055642(5^n)/5)*a(n-1) + 1. - Jason Yuen, Aug 21 2024

More terms from Max Alekseyev, Dec 12 2011

A179197 Numbers k such that there exists no multiple of k whose digits are a permutation of all the digits of all the divisors of k.

Original entry on oeis.org

3, 7, 9, 11, 12, 13, 17, 18, 19, 21, 22, 23, 27, 29, 31, 33, 36, 37, 39, 41, 43, 45, 47, 48, 49, 53, 54, 55, 57, 59, 61, 63, 67, 71, 72, 73, 74, 75, 77, 79, 81, 83, 84, 89, 91, 93, 97, 99, 101, 103, 107, 108, 109, 111, 113, 117, 121, 126, 129, 131, 135, 137, 139, 143, 144

Offset: 1

Jon E. Schoenfield, Jul 02 2010

Numbers k such that A077351(k)=0.

Let s(k) be the sum of the digits of all the divisors of k. The sequence must, of course, include every number k such that 3 divides k but does not divide s(k). Similarly, it must include every k such that 9 divides k but does not divide s(k). The sequence also includes many numbers with relatively few divisors, since the concatenation of their digits offers relatively few opportunities to obtain a multiple of k by permuting them. Of the sequence's 2544 terms below 10000, only four exist that (1) are not primes, (2) are not semiprimes, (3) are not prime powers, (4) are not numbers k that are divisible by 3 but having s(k) not divisible by 3, and (5) are not numbers k that are divisible by 9 but having s(k) not divisible by 9: 242, 2222, 5555, and 7777.

			The divisors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, and 108, and concatenating all their digits gives the 19-digit number 1234691218273654108; no permutation of those 19 digits yields a result that is divisible by 108, so 108 is in the sequence.
The divisors of 14 are 1, 2, 7, and 14, and concatenating all their digits gives the 5-digit number 12714; those 5 digits can be permuted to yield a result (e.g., 21714) that is divisible by 14, so 14 is not in the sequence.

Jon E. Schoenfield, Table of n, a(n) for n=1..2544

Cf. A077351.

cp's OEIS Frontend

A077352 a(n) = (concatenation in ascending order of divisors of 2^n)/2^n.

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A077353 a(n) = (concatenation in ascending order of divisors of 5^n)/5^n.

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A179197 Numbers k such that there exists no multiple of k whose digits are a permutation of all the digits of all the divisors of k.

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