%I #21 Apr 14 2015 10:26:36

%S 2058,10290,22638,26754,34986,39102,47334,51450,52728,59682,63798,

%T 76146,84378,88494,96726,109074,113190,121422,125538,133770,137886,

%U 146118,150234,162582,170814,174930,183162,195510,199626,207858,211974,220206,224322,232554,236670,249018,257250,261366,263640,269598,281946,286062,294294

%N Numbers n for which there exists k < n such that A000203(k) = A000203(n) and A007947(k) = A007947(n), where A000203 gives the sum of divisors, and A007947 gives the squarefree kernel of n.

%C Sequence A255423 sorted into ascending order.

%C Note that both for u = a(17) = 113190 and v = a(22) = 146118, A000203(u) = A000203(v) = 345600.

%C Also, both for w = a(20) = 133770 and x = a(25) = 170814, A000203(w) = A000203(x) = 403200.

%C Question: Does this have any common terms with A255334 ?

%H Antti Karttunen, <a href="/A255335/b255335.txt">Table of n, a(n) for n = 1..2434</a>

%o (PARI)

%o allocatemem(234567890);

%o A007947(n) = factorback(factorint(n)[, 1]); \\ _Andrew Lelechenko_, May 09 2014

%o upto = (2^24)-4;

%o bigvec = vector(upto);

%o i=0; for(n=1, upto, bigvec[n] = Set([]); my(r=A007947(n), s=sigma(n)); if(setsearch(bigvec[r],s), i++; write("b255335.txt", i, " ", n), bigvec[r] = setunion(Set([s]),bigvec[r])));

%o (Scheme, with _Antti Karttunen_'s IntSeq-library. Quite naive implementation.)

%o (define A255335 (MATCHING-POS 1 1 isA255335?))

%o (define (isA255335? n) (let ((sig_n (A000203 n)) (rad_n (A007947 n))) (let loop ((try (- n rad_n))) (cond ((< try rad_n) #f) ((and (= sig_n (A000203 try)) (= rad_n (A007947 try))) #t) (else (loop (- try rad_n)))))))

%Y Subsequence of A013929.

%Y Cf. A000203, A007947.

%Y Cf. also A255334, A255423, A254035.

%K nonn

%O 1,1

%A _Antti Karttunen_, Mar 23 2015, suggested by _Michel Marcus_, Feb 23 2015