A343300 a(n) is p1^1 + p2^2 + ... + pk^k where {p1,p2,...,pk} are the distinct prime factors in ascending order in the prime factorization of n.

0, 2, 3, 2, 5, 11, 7, 2, 3, 27, 11, 11, 13, 51, 28, 2, 17, 11, 19, 27, 52, 123, 23, 11, 5, 171, 3, 51, 29, 136, 31, 2, 124, 291, 54, 11, 37, 363, 172, 27, 41, 354, 43, 123, 28, 531, 47, 11, 7, 27, 292, 171, 53, 11, 126, 51, 364, 843, 59, 136, 61, 963, 52, 2, 174, 1342, 67, 291, 532, 370, 71, 11, 73

Offset

1,2

Comments

From Bernard Schott, May 07 2021: (Start)

a(n) depends only on prime factors of n (see formulas).

Primes are fixed points of this sequence.

Terms are in increasing order in A344023. (End)

Links

Michel Marcus, Table of n, a(n) for n = 1..10000

Formula

a(p^k) = p for p prime and k>=1.

From Bernard Schott, May 07 2021: (Start)

a(A033845(n)) = 11;

a(A033846(n)) = 27;

a(A033847(n)) = 51;

a(A033848(n)) = 123;

a(A033849(n)) = 28;

a(A033850(n)) = 52;

a(A033851(n)) = 54;

a(A288162(n)) = 171. (End)

Example

a(60) = 136 because the distinct prime factors of 60 are {2, 3, 5} and 2^1 + 3^2 + 5^3 = 136.

Maple

a:= n-> (l-> add(l[i]^i, i=1..nops(l)))(sort(map(i-> i[1], ifactors(n)[2]))):
seq(a(n), n=1..73);  # Alois P. Heinz, Sep 19 2024

Mathematica

{0}~Join~Table[Total[(a=First/@FactorInteger[k])^Range@Length@a], {k, 2, 100}]

Prog

(PARI) a(n) = my(f=factor(n)); sum(k=1, #f~, f[k, 1]^k); \\ Michel Marcus, Apr 11 2021

Crossrefs

Cf. A027748, A344023 (terms ordered).

See also A033845-A033851, A288162.

Sequence in context: A367633 A183098 A183101 * A285309 A250096 A345302

Adjacent sequences: A343297 A343298 A343299 * A343301 A343302 A343303

Keyword

nonn

Author

Giorgos Kalogeropoulos, Apr 11 2021

Status

approved