The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A342006 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A342006

Numbers k where the maximal prime exponent in the arithmetic derivative of A276086(k) attains the maximal exponent in A276086(k), where A276086 gives the prime product form of primorial base expansion of its argument.
(history; published version)

#14 by N. J. A. Sloane at Thu Mar 11 21:07:23 EST 2021

STATUS

proposed

approved

#13 by Antti Karttunen at Wed Mar 10 05:14:23 EST 2021

STATUS

editing

proposed

#12 by Antti Karttunen at Wed Mar 10 05:11:48 EST 2021

EXAMPLE

16 is present as A276086(16) = 225, A003415(225) = 240 = 2^4 * 3 * 5, with maximum exponent = 4 >= the maximal exponent 4 in 16 = 2^4.

#11 by Antti Karttunen at Wed Mar 10 04:58:29 EST 2021

NAME

Numbers k for which A328391(k) >= A328114(k); numbers k where the maximal prime exponent in the arithmetic derivative of A276086(k) attains the maximal exponent in A276086(k), where A276086 is gives the prime product form of primorial base expansion of nits argument.

COMMENTS

Numbers k for which A328391(k) >= A328114(k).

#10 by Antti Karttunen at Wed Mar 10 04:57:07 EST 2021

NAME

Numbers k for which A328391(k) >= A328114(k); numbers k where the maximal prime exponent in the arithmetic derivative of A276086(k) attains the maximal exponent in A276086(k), where A276086 is the prime product form of primorial base expansion of n.

#9 by Antti Karttunen at Wed Mar 10 04:51:19 EST 2021

KEYWORD

nonn,look,new

#8 by Antti Karttunen at Wed Mar 10 04:50:22 EST 2021

LINKS

Antti Karttunen, <a href="/A342006/b342006.txt">Table of n, a(n) for n = 1..10000</a>

#7 by Antti Karttunen at Wed Mar 10 04:49:31 EST 2021

PROG

(PARI)

A328114(n) = { my(s=0, p=2); while(n, s = max(s, (n%p)); n = n\p; p = nextprime(1+p)); (s); };

A051903(n) = if((1==n), 0, vecmax(factor(n)[, 2]));

A327860(n) = { my(s=0, m=1, p=2, e); while(n, e = (n%p); m *= (p^e); s += (e/p); n = n\p; p = nextprime(1+p)); (s*m); };

A328391(n) = A051903(A327860(n));

isA342006(n) = (A328391(n) >= A328114(n));

(PARI) isA342006(n) = (0==A342005(n));

CROSSREFS

Cf. A003415, A051903, A276086, A327860, A328114, A328391, A342004, A342018.

STATUS

approved

editing

#6 by Susanna Cuyler at Sat Mar 06 01:34:16 EST 2021

STATUS

proposed

approved

#5 by Antti Karttunen at Fri Mar 05 22:31:13 EST 2021

STATUS

editing

proposed