A289146 Numbers with decimal expansion d_1,d_2,...,d_k that are divisible by sigma_0(d_k) + sigma_1(d_k-1) + ... + sigma_k-1(d_1).

1, 2, 8, 9, 12, 15, 24, 25, 28, 45, 54, 85, 111, 112, 128, 133, 153, 165, 192, 198, 228, 288, 294, 312, 342, 416, 432, 448, 481, 527, 528, 638, 828, 891, 1115, 1127, 1134, 1176, 1215, 1224, 1245, 1278, 1344, 1431, 1472, 1482, 1519, 1652, 1674, 1976, 2114, 2147, 2178, 2184

Offset

1,2

Comments

sigma_k(n) is the sum of the k-th powers of the divisors of n.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

25 is in the sequence as 25 is divisible by sigma_0(5) + sigma_1(2) = 2 + 3 = 5.

Mathematica

f[n_]:=Reverse[IntegerDigits[n]];
g[n_]:=Sum[DivisorSigma[i-1, f[n][[i]]], {i, 1, Length[f[n]]}];
Select[Range[10000], Divisible[#, g[#]]&]
ds[n_]:=Total[DivisorSigma[#[[2]], #[[1]]]&/@Thread[{IntegerDigits[ n], Range[ IntegerLength[n]-1, 0, -1]}]]; Select[Range[3000], Divisible[ #, ds[#]]&] (* Harvey P. Dale, Jul 16 2018 *)

Prog

(PARI) isok(n) = my(d = Vecrev(digits(n))); if (vecmin(d), n % sum(k=1, #d, sigma(d[k], k-1)) == 0); \\ Michel Marcus, Jun 26 2017

Crossrefs

Subsequence of A052382.

Sequence in context: A020676 A086678 A359771 * A294374 A066550 A162952

Adjacent sequences: A289143 A289144 A289145 * A289147 A289148 A289149

Keyword

base,nonn

Author

Ivan N. Ianakiev, Jun 26 2017

Status

approved