A057530 n is odd and divisible by number of divisors of n and sum of digits of n.

1, 9, 225, 441, 1521, 2025, 2601, 12321, 40401, 62001, 99225, 103041, 251001, 321489, 585225, 893025, 1022121, 1108809, 1212201, 1320201, 1946025, 2368521, 2480625, 2772225, 3101121, 3744225, 4473225, 4862025, 5517801, 6125625

Offset: 1

Author

Asher Auel, Sep 03 2000

Keywords

• nonn
• easy
• base

Comments

For most values (except 9,2025 and 99225) number of divisors of n = sum of digits of n, see A057531.

The above comment is wrong: for 16 out of the first 34 terms of the sequence, the number of divisors of n does not equal the sum of the digits of n. - Harvey P. Dale, Dec 31 2015

Since A000005(n) is odd, n must be a square. - Robert Israel, Oct 31 2019

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A005349, A033950, A057529.

Programs

Magma

[k:k in [1..6000001 by 2]| IsIntegral(k/NumberOfDivisors(k)) and IsIntegral(k/&+Intseq(k))]; // Marius A. Burtea, Oct 31 2019

Maple

filter:= proc(m) local n;
  n:= m^2;
  n mod numtheory:-tau(n) = 0 and n mod convert(convert(n,base,10),`+`) = 0
end proc:
map(`^`, select(filter, [seq(i,i=1..10000,2)]),2); # Robert Israel, Oct 31 2019

Mathematica

Select[Range[1,5*10^6,2],Divisible[#,DivisorSigma[0,#]] && Divisible[ #,Total[ IntegerDigits[#]]]&] (* Harvey P. Dale, Dec 31 2015 *)

Extensions

More terms from Harvey P. Dale, Dec 31 2015