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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.
3
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
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).
Sequence in context: A367633 A183098 A183101 * A285309 A250096 A345302
KEYWORD
nonn
AUTHOR
STATUS
approved