A255335 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.

2058, 10290, 22638, 26754, 34986, 39102, 47334, 51450, 52728, 59682, 63798, 76146, 84378, 88494, 96726, 109074, 113190, 121422, 125538, 133770, 137886, 146118, 150234, 162582, 170814, 174930, 183162, 195510, 199626, 207858, 211974, 220206, 224322, 232554, 236670, 249018, 257250, 261366, 263640, 269598, 281946, 286062, 294294

Offset

1,1

Comments

Sequence A255423 sorted into ascending order.

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

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

Question: Does this have any common terms with A255334 ?

Links

Antti Karttunen, Table of n, a(n) for n = 1..2434

Prog

(PARI)
allocatemem(234567890);
A007947(n) = factorback(factorint(n)[, 1]); \\ Andrew Lelechenko, May 09 2014
upto = (2^24)-4;
bigvec = vector(upto);
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])));
(Scheme, with Antti Karttunen's IntSeq-library. Quite naive implementation.)
(define A255335 (MATCHING-POS 1 1 isA255335?))
(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)))))))

Crossrefs

Subsequence of A013929.

Cf. A000203, A007947.

Cf. also A255334, A255423, A254035.

Sequence in context: A074996 A252112 A045055 * A255423 A202418 A069427

Adjacent sequences: A255332 A255333 A255334 * A255336 A255337 A255338

Keyword

nonn

Author

Antti Karttunen, Mar 23 2015, suggested by Michel Marcus, Feb 23 2015

Status

approved