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

Author

Giorgos Kalogeropoulos, Apr 11 2021

Keywords

• nonn

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)

Examples

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

Links

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

Crossrefs

Cf. A027748, A344023 (terms ordered).

See also A033845-A033851, A288162.

Programs

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}]

PARI

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

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)