cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A037276 Start with 1; for n>1, replace n with the concatenation of its prime factors in increasing order.

Original entry on oeis.org

1, 2, 3, 22, 5, 23, 7, 222, 33, 25, 11, 223, 13, 27, 35, 2222, 17, 233, 19, 225, 37, 211, 23, 2223, 55, 213, 333, 227, 29, 235, 31, 22222, 311, 217, 57, 2233, 37, 219, 313, 2225, 41, 237, 43, 2211, 335, 223, 47, 22223, 77, 255, 317, 2213, 53, 2333
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Examples

			If n = 2^3*5^5*11^2 = 3025000, a(n) = 222555551111 (n=2*2*2*5*5*5*5*5*11*11, then remove the multiplication signs).

Links

Crossrefs

Cf. A037274, A048985, A067599, A080670, A084796. Different from A073646.
Cf. also A027746, A289660 (a(n)-n).

Programs

  • Haskell
    a037276 = read . concatMap show . a027746_row
-- Reinhard Zumkeller, Apr 03 2012
  • Maple
    # This is for n>1
read("transforms") ;
A037276 := proc(n)
    local L,p ;
    L := [] ;
    for p in ifactors(n)[2] do
        L := [op(L),seq(op(1,p),i=1..op(2,p))] ;
    end do:
    digcatL(L) ;
end proc: # R. J. Mathar, Oct 29 2012
  • Mathematica
    co[n_, k_] := Nest[Flatten[IntegerDigits[{#, n}]] &, n, k - 1]; Table[FromDigits[Flatten[IntegerDigits[co @@@ FactorInteger[n]]]], {n, 54}] (* Jayanta Basu, Jul 04 2013 *)
FromDigits@ Flatten@ IntegerDigits[Table[#1, {#2}] & @@@ FactorInteger@ #] & /@ Range@ 54 (* Michael De Vlieger, Jul 14 2015 *)
  • PARI
    a(n)={ n<4 & return(n); for(i=1,#n=factor(n)~, n[1,i]=concat(vector(n[2,i],j,Str(n[1,i])))); eval(concat(n[1,]))}  \\ M. F. Hasler, Jun 19 2011
  • Python
    from sympy import factorint
def a(n):
    f=factorint(n)
    l=sorted(f)
    return 1 if n==1 else int("".join(str(i)*f[i] for i in l))
print([a(n) for n in range(1, 101)]) # Indranil Ghosh, Jun 23 2017

A085307 a(1) = 1; for n > 1, concatenate distinct prime factors of n in decreasing order.

Original entry on oeis.org

1, 2, 3, 2, 5, 32, 7, 2, 3, 52, 11, 32, 13, 72, 53, 2, 17, 32, 19, 52, 73, 112, 23, 32, 5, 132, 3, 72, 29, 532, 31, 2, 113, 172, 75, 32, 37, 192, 133, 52, 41, 732, 43, 112, 53, 232, 47, 32, 7, 52, 173, 132, 53, 32, 115, 72, 193, 292, 59, 532, 61, 312, 73, 2, 135, 1132, 67
Offset: 1

Views

Author

Labos Elemer, Jun 27 2003

Keywords

Comments

n and a(n) have the same parity.

Examples

			m = 100 = 2*2*5*5 -> {2,5} -> {5,2} -> 52 = a(100);
a(510510) = 1713117532, while A084317(510510) = 2357111317.

Links

Crossrefs

In A084317 the order of factors is increasing.
Cf. A084317, A084318, A084319, A085308, A085309, A084796, A084797.

Programs

  • Maple
    with(numtheory):
a:= n-> parse(cat(`if`(n=1, 1, sort([factorset(n)[]], `>`)[]))):
seq(a(n), n=1..100);  # Alois P. Heinz, May 02 2016
  • Mathematica
    f[n_] := FromDigits[ Flatten[ IntegerDigits /@ Reverse[ Flatten[ Table[ # [[1]], {1}] & /@ FactorInteger[n]]]]]; Table[ f[n], {n, 1, 70}]
Table[FromDigits[Flatten[IntegerDigits/@Reverse[FactorInteger[n][[All, 1]]]]],{n,90}] (* Harvey P. Dale, Oct 10 2017 *)

Formula

Algorithm:
1. factorize n;
2. order prime factors by decreasing size;
3. concatenate prime factors and interpret the result as a decimal number.

Extensions

Edited by Robert G. Wilson v, Jul 15 2003

A084797 Greatest number formed by concatenating prime factors of n in base 10.

Original entry on oeis.org

1, 2, 3, 22, 5, 32, 7, 222, 33, 52, 11, 322, 13, 72, 53, 2222, 17, 332, 19, 522, 73, 211, 23, 3222, 55, 213, 333, 722, 29, 532, 31, 22222, 311, 217, 75, 3322, 37, 219, 313, 5222, 41, 732, 43, 2211, 533, 232, 47, 32222, 77, 552, 317, 2213, 53, 3332, 511, 7222
Offset: 1

Views

Author

N. J. A. Sloane, Jul 19 2003

Keywords

Links

Crossrefs

Different from A084796. Cf. A073646.

Programs

  • Maple
    with(combinat):
a:= n-> `if`(n=1, 1, max(map(x-> parse(cat(x[])),
    permute([seq(i[1]$i[2], i=ifactors(n)[2])]))[])):
seq(a(n), n=1..100);  # Alois P. Heinz, May 02 2016

Extensions

More terms from Alois P. Heinz, May 02 2016

A130975 a(n) = sum of numbers without digit 1 and with product of digits = n-th 7-smooth number.

Original entry on oeis.org

0, 2, 3, 26, 5, 61, 7, 296, 42, 77, 942, 99, 88, 3264, 1108, 1098, 110, 13338, 55, 465, 1342, 2341, 35906, 132, 21869, 14806, 2807, 1375, 179141, 77, 1332, 16826, 17494, 45546, 1619, 394746, 3108, 376165, 1443, 192545, 5097, 53100, 49989, 2326191
Offset: 1

Views

Author

Philippe Lallouet (philip.lallouet(AT)wanadoo.fr), Aug 23 2007

Keywords

Examples

			First 7-smooth number is 1. Sum of numbers without digit 1 and with product of digits = 1 is 0 since there are no such numbers. Hence a(1) = 0.
Eighth 7-smooth number is 8, numbers without digit 1 and with product of digits = 8 are 8, 24, 42, 222. These sum to 296, hence a(8) = 296.
Eleventh 7-smooth number is 12, numbers without digit 1 and with product of digits = 12 are 26, 34, 43, 62, 223, 232, 322. These sum to 942, hence a(11) = 942.
Fifteenth 7-smooth number is 18, numbers without digit 1 and with product of digits = 18 are 29, 36, 63, 92, 233, 323, 332. These sum to 1108, hence a(15) = 1108.

Links

Crossrefs

Cf. A002473 (7-smooth numbers), A084796 (concatenation of prime factors of n in decreasing order).

Extensions

Edited, corrected and extended by Klaus Brockhaus, Aug 26 2007
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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