A371240 The sum of divisors of the zeroless numbers in base 3 (A032924).

1, 3, 7, 6, 8, 15, 14, 24, 31, 18, 36, 24, 31, 42, 90, 42, 44, 84, 57, 93, 98, 54, 68, 126, 144, 72, 140, 96, 80, 186, 133, 186, 224, 156, 252, 132, 160, 204, 266, 150, 152, 300, 158, 240, 378, 192, 306, 240, 252, 312, 212, 378, 324, 264, 230, 432, 450, 234, 432

Offset: 1

Author

Amiram Eldar, Mar 16 2024

Keywords

• nonn
• base
• easy

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• William D. Banks and Igor E. Shparlinski, Arithmetic properties of numbers with restricted digits, Acta Arithmetica, Vol. 112, No. 4 (2004), pp. 313-332; alternative link.

Crossrefs

Cf. A000203, A032924, A214549, A371239, A371241.

Programs

Mathematica

DivisorSigma[1, Select[Range[300], !MemberQ[IntegerDigits[#, 3], 0] &]]

PARI

lista(kmax) = for(k = 1, kmax, if(vecmin(digits(k, 3)) > 0, print1(sigma(k), ", ")));

Formula

a(n) = A000203(A032924(n)).

Asymptotic mean of the abundancy index of A032924: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k)/A032924(k) = 4*Pi^2/27 = 1.462163... (A214549) (Banks and Shparlinski, 2004).