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 1-3 of 3 results.

A101701 Numbers n such that n = sum of the reversals of divisors of n.

Original entry on oeis.org

1, 207321, 890827, 7591023, 18368601, 4885292403
Offset: 1

Views

Author

Farideh Firoozbakht, Dec 23 2004

Keywords

Comments

a(7) > 10^11. - Donovan Johnson, Dec 27 2013

Examples

			18368601 is in the sequence because divisors of 18368601 are 1, 3, 6122867, 18368601 and 18368601 = 1 + 3 + 7682216 + 10686381.
		

Crossrefs

Programs

  • Mathematica
    Do[h = Divisors[n]; l = Length[h]; If[n == Sum[ FromDigits[Reverse[IntegerDigits[h[[k]]]]], {k, l}], Print[n]], {n, 370000000}]
  • Python
    from sympy import divisors
    A101701_list = [n for n in range(1,10**6) if n == sum([int(d) for d in (str(x)[::-1] for x in divisors(n))])]
    # Chai Wah Wu, Dec 06 2014

Extensions

a(6) from Donovan Johnson, Dec 07 2008

A244251 Numbers k such that if m = (sum of the reverses of the aliquot parts of k) then k = (sum of the reverses of the aliquot parts of m).

Original entry on oeis.org

6, 98, 145, 244, 285, 133857
Offset: 1

Views

Author

Paolo P. Lava, Dec 09 2014

Keywords

Comments

A072228 is a subsequence of this sequence.

Examples

			Aliquot parts of 98 are 1, 2, 7, 14, 49 and the sum of their reverses is 1 + 2 + 7 + 41 + 94 = 145. Aliquot parts of 145 are 1, 5, 29 and the sum of their reverses is 1 + 5 + 92 = 98.
		

Crossrefs

Cf. A072228.

Programs

  • Maple
    with(numtheory): T:=proc(w) local x,y,z; x:=0; y:=w;
    for z from 1 to ilog10(w)+1 do x:=10*x+(y mod 10); y:=trunc(y/10); od; x; end:
    P:=proc(q) local a,b,k,n; for n from 1 to q do
    a:=sort([op(divisors(n))]); b:=add(T(a[k]),k=1..nops(a)-1); a:=sort([op(divisors(b))]); b:=add(T(a[k]),k=1..nops(a)-1);
    if b=n then print(n); fi; od; end: P(10^12);

A254009 Numbers that divide the sum of the reverse of their aliquot parts (A069250).

Original entry on oeis.org

1, 6, 244, 285, 944, 1242, 3738, 22644, 37686, 58950, 85512, 124944, 130410, 133857, 235644, 3202101, 5367582, 5663697, 45165231, 141635817, 214939686, 736140702, 2395863144, 4992033177, 28406362140, 30364415451
Offset: 1

Views

Author

Paolo P. Lava, Jan 22 2015

Keywords

Comments

A072228 is a subsequence. - Paolo P. Lava, Nov 09 2018

Examples

			Aliquot parts of 944 are 1, 2, 4, 8, 16, 59, 118, 236, 472 and the sum of their reverse is 1 + 2 + 4 + 8 +61 + 95 + 811 + 632 + 274 = 1888. Finally, 1888 / 944 = 2.
		

Crossrefs

Programs

  • Maple
    with(numtheory):
    T:=proc(w) local x,y,z; x:=w; y:=0;
    for z from 1 to ilog10(x)+1 do y:=10*y+(x mod 10); x:=trunc(x/10); od; y; end:
    P:=proc(q) local a,b,k; global n;
    for n from 1 to q do a:=sort([op(divisors(n))]); b:=add(T(a[k]),k=1..nops(a)-1);
    if type(b/n,integer) then print(n); fi; od; end: P(10^9);
  • PARI
    isok(n) = (sumdiv(n, d, (d != n)* eval(concat(Vecrev(Str(d))))) % n) == 0; \\ Michel Marcus, Feb 27 2015

Extensions

a(16)-a(26) from Lars Blomberg, Feb 27 2015
Showing 1-3 of 3 results.