The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A255423

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The least number k > A255334(n) for which A000203(k) = A000203(A255334(n)) and A007947(k) = A007947(A255334(n)), where A000203 gives the sum of divisors, and A007947 gives the squarefree kernel of n.
(history; published version)

#9 by Charles R Greathouse IV at Tue Jul 19 12:29:59 EDT 2016

STATUS

editing

approved

#8 by Charles R Greathouse IV at Tue Jul 19 12:29:57 EDT 2016

PROG

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

i=0; for(n=1, 2^25, k = nextone(n); if(k, i++; write("b255423.txt", i, " ", k))); \\ _Andrew Lelechenko_, May 09 2014

STATUS

approved

editing

#7 by N. J. A. Sloane at Tue Apr 14 10:26:55 EDT 2015

STATUS

proposed

approved

#6 by Antti Karttunen at Mon Apr 13 13:16:20 EDT 2015

STATUS

editing

proposed

#5 by Antti Karttunen at Mon Apr 13 13:01:04 EDT 2015

NAME

The next larger least number k > j = A255334(n) for which A000203(k) = A000203(jA255334(n)) and A007947(k) = A007947(jA255334(n)), where A000203 gives the sum of divisors, and A007947 gives the squarefree kernel of n.

#4 by Antti Karttunen at Mon Apr 13 12:38:22 EDT 2015

CROSSREFS

Cf. A000203, A007947, A255334.

Cf. A255334, also A255335 (same sequence sorted into ascending order), A255424 (squarefree kernel of a(n)), A255426 (same terms with but with their squarefree kernel divided out of them).

A255424 (squarefree kernel of a(n)), A255426.

#3 by Antti Karttunen at Mon Apr 06 11:34:28 EDT 2015

LINKS

Antti Karttunen, <a href="/A255423/b255423.txt">Table of n, a(n) for n = 1..6589</a>

FORMULA

a(n) = A255424(n) * A255426(n).

CROSSREFS

Cf. A255334, A255335 (same sequence sorted into ascending order).,

A255424 (squarefree kernel of a(n)), A255426.

#2 by Antti Karttunen at Mon Apr 06 10:49:31 EDT 2015

NAME

allocated The next larger number k > j = A255334(n) for Antti Karttunenwhich A000203(k) = A000203(j) and A007947(k) = A007947(j), where A000203 gives the sum of divisors, and A007947 gives the squarefree kernel of n.

DATA

2058, 10290, 22638, 26754, 34986, 39102, 47334, 51450, 59682, 52728, 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, 269598, 281946, 286062, 294294

OFFSET

1,1

PROG

(PARI)

A007947(n) = factorback(factorint(n)[, 1]); \\ Andrew Lelechenko, May 09 2014

nextone(n) = { if(!n, return(0)); my(r=A007947(n), s=sigma(n), k=n+r); while(k<s, if((sigma(k) == s)&&(A007947(k) == r), return(k), k = k+r)); return(0); };

i=0; for(n=1, 2^25, k = nextone(n); if(k, i++; write("b255423.txt", i, " ", k)));

CROSSREFS

Cf. A255334, A255335 (same sequence sorted into ascending order).

KEYWORD

allocated

nonn

AUTHOR

Antti Karttunen, Apr 06 2015

STATUS

approved

editing

#1 by Antti Karttunen at Sun Feb 22 11:22:18 EST 2015

NAME

allocated for Antti Karttunen

KEYWORD

allocated

STATUS

approved