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A337183 If n is composite, a(n) is the number represented by the list of prime factors of n (with multiplicity, sorted in nondecreasing order) in base the sum of that list.  If n is prime, a(n) = n. 3
2, 3, 10, 5, 13, 7, 86, 21, 19, 11, 115, 13, 25, 29, 1170, 17, 155, 19, 185, 37, 37, 23, 1641, 55, 43, 273, 271, 29, 235, 31, 22222, 53, 55, 67, 2233, 37, 61, 61, 2931, 41, 331, 43, 491, 401, 73, 47, 32211, 105, 353, 77, 625, 53, 3061, 91, 4765, 85, 91, 59, 3785, 61, 97, 553, 542906, 103, 571, 67 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

If p is prime, a(p^k) = p*((k*p)^k-1)/(k*p-1).

If n = p*q with primes p <= q, a(n) = p^2 + p*q + q.

LINKS

Robert Israel, Table of n, a(n) for n = 2..10000

EXAMPLE

For n = 12, the list of prime factors is [2,2,3], the base is 2+2+3=7, and a(12) = 223_7 = 115.

MAPLE

f:= proc(n) local F, b, i;

  F:= sort(map(t -> t[1]$t[2], ifactors(n)[2]), `>`);

  b:= convert(F, `+`);

  (add(F[i]*b^(i-1), i=1..nops(F)));

end proc:

map(f, [$2..100]);

MATHEMATICA

Array[If[PrimeQ@ #, #, FromDigits[#, Total[#]] &@ Flatten[ConstantArray @@@ FactorInteger[#]]] &, 66, 2] (* Michael De Vlieger, Jan 29 2021 *)

CROSSREFS

Sequence in context: A216937 A230625 A048985 * A112417 A139693 A182076

Adjacent sequences:  A337180 A337181 A337182 * A337184 A337185 A337186

KEYWORD

nonn,base,look

AUTHOR

J. M. Bergot and Robert Israel, Jan 29 2021

STATUS

approved

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Last modified April 19 07:36 EDT 2021. Contains 343109 sequences. (Running on oeis4.)