A367918 Numbers formed by concatenating n with the distinct prime factors of n, left to right, smallest factors to largest, with a(1) = 10.

10, 22, 33, 42, 55, 623, 77, 82, 93, 1025, 1111, 1223, 1313, 1427, 1535, 162, 1717, 1823, 1919, 2025, 2137, 22211, 2323, 2423, 255, 26213, 273, 2827, 2929, 30235, 3131, 322, 33311, 34217, 3557, 3623, 3737, 38219, 39313, 4025, 4141, 42237, 4343, 44211, 4535, 46223, 4747, 4823, 497, 5025, 51317, 52213

Offset

1,1

Links

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

Example

a(2) =  22 as 2 has only one prime factor, which is 2;
a(3) =  33 as 3 has only one prime factor, which is 3;
a(4) =  42 as 4 has only one distinct prime factor, which is 2;
a(5) =  55 as 5 has only one prime factor, which is 5;
a(6) = 623 as 6 has two distinct prime factors, which are 2 and 3; etc.

Maple

f:= proc(n) local P;
  P:= sort(convert(numtheory:-factorset(n), list));
  parse(cat(n, op(P)))
end proc:
f(1):= 10:
mao(f, [$1..100]); # Robert Israel, Mar 04 2024

Mathematica

a[1] = 1; a[n_Integer?Positive] := Module[{p, t}, p = Sort[DeleteDuplicates[FactorInteger[n][[All, 1]]]]; t = FromDigits[Flatten[IntegerDigits /@ Prepend[p, n]]]; t]; Table[a[n], {n, 1, 48}] (* Robert P. P. McKone, Dec 04 2023 *)

Crossrefs

Cf. A027748, A037274.

Sequence in context: A007366 A302280 A350627 * A109958 A053361 A214153

Adjacent sequences: A367915 A367916 A367917 * A367919 A367920 A367921

Keyword

base,nonn,look

Author

Eric Angelini, Dec 04 2023

Status

approved