A216687 Odd numbers > 10 that can be written as m*s - m + 1, where s is the sum of their digits and m >= 1.

11, 13, 19, 21, 25, 31, 37, 41, 43, 49, 51, 55, 61, 71, 73, 81, 85, 91, 101, 103, 109, 111, 113, 115, 121, 127, 133, 141, 145, 151, 153, 157, 163, 181, 191, 193, 199, 201, 205, 211, 217, 221, 223, 225, 229, 231, 235, 241, 253, 265, 267, 271, 281, 289, 301, 307, 309

Offset

1,1

Comments

The corresponding values of m: 10, 4, 6, 10, 4, 10, 4, 10, 7, 4, 10, 6, 10, 10, 8, 10, 7, 10, 100, 34, 12, 55, 28, 19, 40, 14, 22, 28, 16, 25, 19, 13, 18, 20, 19, 16, 11, 100, 34, 70, 24, 55, 37, 28, 19, 46, 26, 40, 28, 22, 19, 30, 28, 16, 100, 34, 28.

This property seems to be very interesting: some primes have it, some don't (from the first 60 primes bigger than 10, 29 have this property and 31 haven't, which is a surprisingly equal proportion); some odd composite numbers have it, some don't (just less than a third from the first 60 such numbers have it), but most of Carmichael numbers checked have it; the first 20 such numbers will be enumerated, with the corresponding value of n in the brackets: 1105(184), 1729(96), 2465(154), 2821(235), 6601(550), 8911(495), 10585(588), 15841(880), 29341(1630), 41041(4560), 46657(1728), 52633(2924), 62745(2728), 101101(33700), 115921(6440), 126217(7012), 172081(9560), 188461(10470), 252601(16840), 294409(10904).

From the first 25 Carmichael numbers, just 5 of them (561, 63973, 75361, 162401 and 278545) lack this property.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Carmichael Number

Prog

(PARI) is(n)=n%2 && n>9 && Mod(n, sumdigits(n)-1)==1 \\ Charles R Greathouse IV, Dec 07 2014

Crossrefs

Cf. A002997.

Sequence in context: A136491 A357074 A268487 * A005360 A269806 A062019

Adjacent sequences: A216684 A216685 A216686 * A216688 A216689 A216690

Keyword

nonn,base,easy

Author

Marius Coman, Sep 14 2012

Status

approved