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.

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

Cf. A069250, A072228, A007691, A254008.

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

A069192 Sum of the reversals of the divisors of n.

Original entry on oeis.org

1, 3, 4, 7, 6, 12, 8, 15, 13, 9, 12, 37, 32, 51, 60, 76, 72, 102, 92, 15, 23, 36, 33, 87, 58, 96, 85, 137, 93, 72, 14, 99, 48, 117, 66, 190, 74, 177, 128, 27, 15, 96, 35, 84, 123, 99, 75, 232, 102, 66, 90, 125, 36, 219, 72, 210, 170, 180, 96, 105, 17, 42, 68, 145, 93, 144, 77, 207, 132, 117, 18, 267, 38, 123, 169, 248
Offset: 1

Views

Author

Joseph L. Pe, Apr 19 2002

Keywords

Examples

			The divisors of 10 are 1,2,5,10, which reversed are 1,2,5,1, summing to 9. Therefore a(10) = 9.

Links

Crossrefs

Cf. A000203, A069250.

Programs

  • Maple
    read("transforms") ;
A069192 := proc(n)
        add(digrev(d),d=numtheory[divisors](n)) ;
end proc: # R. J. Mathar, Sep 09 2015
  • Mathematica
    f[n_] := FromDigits[Reverse[IntegerDigits[n]]]; g[n_] := Apply[Plus, Map[f, Divisors[n]]]; Table[g[i], {i, 1, 40}]
  • Python
    def A069192(n):
    s=0
    for i in range(1,n+1):
        if n%i==0: s+=int(str(i)[::-1])
    return s # Indranil Ghosh, Feb 10 2017

Extensions

Added more terms, corrected offset. - N. J. A. Sloane, May 19 2013

A163122 Composite numbers for which the sum of proper divisors equals the sum of the digit-reversed proper divisors.

Original entry on oeis.org

4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 21, 22, 25, 27, 33, 35, 44, 49, 55, 66, 77, 88, 99, 121, 202, 242, 262, 302, 303, 362, 363, 382, 393, 403, 404, 453, 484, 505, 524, 543, 573, 605, 606, 626, 655, 689, 706, 707, 726, 746, 755, 766, 783, 786, 808, 840, 847, 905
Offset: 1

Views

Author

Claudio Meller, Jul 21 2009

Keywords

Examples

			840 is in the sequence: the sum of its proper divisors is
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 10 + 12 + 14 + 15 + 20 + ... + 280 + 420 = A001065(840) = 2040,
and the sum of the reversed proper divisors is
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 1 + 21 + 41 + 51 + 2 + ... + 82 + 24 = A069250(840) = 2040.

Links

Programs

  • Maple
    read("transforms") ; A001065 := proc(n) numtheory[sigma](n)-n ; end:
A069250 := proc(n) local pdvs ,a,d ; pdvs := numtheory[divisors](n) minus {n} ; a := 0 ; for d in pdvs do a := a+digrev(d) ; od: a ; end:
for n from 4 to 1000 do if not isprime(n) and A001065(n) = A069250(n) then printf("%d,",n) ; fi; od: # R. J. Mathar, Jul 27 2009
  • Mathematica
    Select[Range[1000],CompositeQ[#]&&DivisorSigma[1,#]-#==Total[IntegerReverse/@ Most[ Divisors[ #]]]&] (* Harvey P. Dale, Oct 12 2023 *)

Formula

{n : n in A002808, and A001065(n) = A069250(n)}. - R. J. Mathar, Jul 27 2009

Extensions

Keyword:base added by R. J. Mathar, Jul 27 2009

A225684 Nonpalindromic numbers n with property that the sum of the reversed divisors of n is equal to n+1.

Original entry on oeis.org

965, 8150, 12966911, 625261742
Offset: 1

Views

Author

N. J. A. Sloane, May 19 2013

Keywords

Comments

Palindromes are excluded because palindromic primes automatically have this property, and palindromic nonprimes never have it.
Call a number "quasi-perfect" or "slightly excessive" if sigma(n) = 2n+1 (cf. A000203). It is conjectured that no quasi-perfect number exists. The present sequence is a variation that certainly has at least four terms.
a(5) > 10^11. - Donovan Johnson, May 26 2013
a(5) > 10^12. - Giovanni Resta, Aug 19 2019

Examples

			The divisors of 965 are 1, 5, 193, 965, and reversing and adding produces 1 + 5 + 391 + 569 = 966.

Links

Crossrefs

Cf. A069192, A069250, A000203.

Programs

  • Python
    from sympy import divisors
def ispal(n): s = str(n); return s == s[::-1]
def ok(n):
  return not ispal(n) and n+1 == sum(int(str(d)[::-1]) for d in divisors(n))
print([m for m in range(10**4) if ok(m)]) # Michael S. Branicky, Jan 25 2021

Extensions

a(4) from Donovan Johnson, May 19 2013
Showing 1-4 of 4 results.

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

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