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

Author

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

Keywords

• nonn

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

Crossrefs

Subsequence of A013929.

Cf. A000203, A007947.

Cf. also A255334, A255423, A254035.

Programs

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)))))))