A306360 Numbers k such that A101337(k)/k is an integer.

1, 2, 3, 4, 5, 6, 7, 8, 9, 153, 370, 371, 407, 459, 1634, 8208, 9474, 13598, 48495, 54748, 92727, 93084, 119564, 174961, 306979, 548834, 1741725, 3194922, 4210818, 9800817, 9926315, 12720569, 24678050, 24678051, 88593477, 144688641, 146511208

Offset

1,2

Comments

A005188 is a subsequence of this sequence.

Sequence is finite. In particular, a(n) < 10^60. If k >= 10^60, then A101337(k) < k. - Chai Wah Wu, Feb 26 2019

Links

Giovanni Resta, Table of n, a(n) for n = 1..109 (full sequence; first 56 terms from Chai Wah Wu)

Barry Fagin, Idempotent Factorizations of Square-free Integers, Preprints (2019).

Example

For k = 1, (1^1)/1 = 1;
for k = 459, (4^3 + 5^3 + 9^3) / 459 = 2.

Mathematica

Select[Range[10^6], IntegerQ[Total[IntegerDigits[#]^IntegerLength[#]]/#] &] (* Michael De Vlieger, Aug 01 2019 *)

Prog

(PARI) isok(n) = frac(A101337(n)/n) == 0; \\ Michel Marcus, Feb 11 2019
(PARI) select( is(n)=!(A101337(n)%n), [0..999]) \\ M. F. Hasler, Nov 17 2019
(Python)
A306360_list, k = [], 1
while k < 10**9:
    s = str(k)
    l, c = len(s), 0
    for i in range(l):
        c = (c + int(s[i])**l) % k
    if c == 0:
        A306360_list.append(k)
    k += 1 # Chai Wah Wu, Feb 26 2019

Crossrefs

Cf. A005188, A101337, A306354, A306361.

Sequence in context: A151544 A032561 A342157 * A023052 A005188 A032569

Adjacent sequences: A306357 A306358 A306359 * A306361 A306362 A306363

Keyword

nonn,base,fini,full

Author

Ctibor O. Zizka, Feb 10 2019

Extensions

a(22)-a(37) from Daniel Suteu, Feb 10 2019

Status

approved