A159000 -id:A159000 - cp's OEIS frontend

A159001 First part "s" of A159000(n).

33, 19, 3, 5, 1209, 39, 4515, 54, 628, 695, 7, 3008, 374, 5, 17, 46, 5, 119, 1, 193933, 2438553, 24, 37, 3776, 54, 582, 1010472, 1067915, 2248, 46, 8080756, 811, 98, 10089515, 10538, 267794, 333070617, 334134, 561868, 159, 176, 1, 337435, 3, 37, 4677, 801, 101123, 13394006, 1714212, 377

Offset: 1

Farideh Firoozbakht, Jun 07 2009

			A159000(1) = 3360 = phi(33)*sigma(60) so a(1) = 33.
A159000(5) = 451584 = phi(4515)*sigma(84) so a(5) = 4515.

Cf. A000010, A000203, A159000.

a(n) = floor(A159000(n)/10^l), where l is such that phi(floor(A159000(n)/10^l)) * sigma(A159000(n)%10^l) = A159000(n). - Max Alekseyev, May 26 2025

a(3), a(4), a(11) and more terms added using A159000 by Amiram Eldar, Mar 18 2024

a(34)-a(51) from Max Alekseyev, May 26 2025

A253824 Numbers m = concat(s,t) such that m = sigma(s) * sigma(t), where sigma(x) is the sum of the divisors of x.

Original entry on oeis.org

540, 2352, 28224, 82890, 737856, 1524096, 1531152, 3429216, 17062920, 22264200, 23268600, 49447728, 104941200, 162496048, 197499456, 267450144, 502334784, 619672032, 2347826040, 2942021520, 4045874976, 4302305280, 9876226752, 22712348160, 24705882348, 33114541824, 34144545792, 45916416000

Offset: 1

Paolo P. Lava, Jan 15 2015

			540 = concat(5,40) -> sigma(5) = 6, sigma(40) = 90 and 6*90 = 540.
2352 = concat(23,52) -> sigma(23) = 24, sigma(52) = 98 and 24*98 = 2352.
28224 = concat(28,224) -> sigma(28) = 56, sigma(224) = 504 and 56*504 = 28222.
82890 = concat(8,2890) -> sigma(8) = 15, sigma(2890) = 5526 and 15*5526 = 82890.

Max Alekseyev, Table of n, a(n) for n = 1..40

Cf. A000203, A159000, A253825, A260144.

with(numtheory): P:=proc(q) local s, t, k, n;
for n from 1 to q do for k from 1 to ilog10(n) do s:=n mod 10^k; t:=trunc(n/10^k); if s*t>0 then if sigma(s)*sigma(t)=n
then print(n); break; fi; fi; od; od; end: P(10^6);

fQ[n_] := Block[{idn = IntegerDigits@ n, lng = Floor@ Log10@ n}, MemberQ[ Table[ DivisorSigma[1, FromDigits@ Take[ idn, {1, i}]] DivisorSigma[1, FromDigits@ Take[ idn, {i + 1, lng + 1}]], {i, lng}], n]]; k = 1; lst = {}; While[k < 1310000001, If[fQ@ k, AppendTo[ lst, k]; Print@ k]; k++] (* Robert G. Wilson v, Jan 19 2015 *)

isok(n) = {len = #Str(n); for (k=1, len-1, na = n\10^k; nb = n % 10^k; if (nb && (n == sigma(na)*sigma(nb)), return (1)););} \\ Michel Marcus, Jan 15 2015

a(8) from Michel Marcus, Jan 15 2015
a(9)-a(17) from Robert G. Wilson v, Jan 18 2015
Missing a(14) and a(19)-a(23) from Giovanni Resta, Jul 17 2015
Terms a(24) onward from Max Alekseyev, May 25 2025

A260144 Numbers k such that there exist two numbers a and b where k = a.b = sigma(a)*phi(b) ("." means concatenation).

Original entry on oeis.org

1568, 14049280, 140492800, 368089904, 506300928, 1404928000, 14049280000, 124856008704, 140492800000, 1404928000000

Offset: 1

Paolo P. Lava and Giovanni Resta, Jul 17 2015

The sequence is infinite because, for m>0, 14049280*10^m = sigma(1404) * phi(9280*10^m).

			1568 is in the sequence because 1568 = sigma(156) * phi(8).

Cf. A000010, A000203, A159000, A253824.

a(7)-a(10) from Max Alekseyev, May 26 2025

cp's OEIS Frontend

A159001 First part "s" of A159000(n).

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A253824 Numbers m = concat(s,t) such that m = sigma(s) * sigma(t), where sigma(x) is the sum of the divisors of x.

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A260144 Numbers k such that there exist two numbers a and b where k = a.b = sigma(a)*phi(b) ("." means concatenation).

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