The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A368920 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A368920

Number of terms of A368904 less than 10^n, where A368904 gives the numbers k for which there is no prime p such that p^p divides A342001(k).
(history; published version)

#10 by Michael De Vlieger at Sun Jan 14 20:35:10 EST 2024

STATUS

proposed

approved

#9 by Jon E. Schoenfield at Sun Jan 14 15:53:17 EST 2024

STATUS

editing

proposed

Discussion

Sun Jan 14

16:02

Antti Karttunen: Yes, better, thanks!

#8 by Jon E. Schoenfield at Sun Jan 14 15:52:37 EST 2024

NAME

Number of terms of A368904 less than 10^n, where A368904 gives the numbers k for which there is no such prime p such that p^p would divide divides A342001(nk).

STATUS

proposed

editing

Discussion

Sun Jan 14

15:53

Jon E. Schoenfield: Is this correct?

#7 by Antti Karttunen at Sun Jan 14 15:49:48 EST 2024

STATUS

editing

proposed

#6 by Antti Karttunen at Sun Jan 14 15:09:58 EST 2024

NAME

Number of terms of A368904 less than 10^n, where A368904 gives the numbers k for which there is no such prime p that p^p would divide A342001(n), where A342001(n) is the arithmetic derivative of n divided by its greatest common divisor with n.

STATUS

approved

editing

Discussion

Sun Jan 14

15:49

Antti Karttunen: Deleted the incorrect description from the name.

#5 by Michael De Vlieger at Sun Jan 14 12:38:56 EST 2024

STATUS

proposed

approved

#4 by Antti Karttunen at Sun Jan 14 12:38:53 EST 2024

STATUS

editing

proposed

#3 by Antti Karttunen at Sun Jan 14 12:35:27 EST 2024

PROG

(PARI)\\ Needs also program from A368914:

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

A003557(n) = (n/factorback(factorint(n)[, 1]));

A342001(n) = (A003415(n) / A003557(n));

A359550(n) = { my(f = factor(n)); prod(k=1, #f~, (f[k, 2]<f[k, 1])); };

A368914(n) = ((n>1)&&A359550(A342001(n)));

#2 by Antti Karttunen at Sun Jan 14 11:13:20 EST 2024

NAME

allocated Number of terms of A368904 less than 10^n, where A368904 gives the numbers k for Antti Karttunenwhich there is no such prime p that p^p would divide A342001(n), where A342001(n) is the arithmetic derivative of n divided by its greatest common divisor with n.

DATA

8, 80, 781, 7752, 77275, 772088, 7718342, 77161311

OFFSET

1,1

PROG

(PARI)

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

A003557(n) = (n/factorback(factorint(n)[, 1]));

A342001(n) = (A003415(n) / A003557(n));

A359550(n) = { my(f = factor(n)); prod(k=1, #f~, (f[k, 2]<f[k, 1])); };

A368914(n) = ((n>1)&&A359550(A342001(n)));

tp=10; s=0; for(n=1, 10^10, s+=A368914(n); if(1+n==tp, print1(s, ", "), if(n==tp, tp *= 10)));

CROSSREFS

Cf. A003415, A342001, A359550, A368904, A368914.

Cf. also A368911, A368919.

KEYWORD

allocated

nonn

AUTHOR

Antti Karttunen, Jan 14 2024

STATUS

approved

editing

#1 by Antti Karttunen at Tue Jan 09 17:48:56 EST 2024

NAME

allocated for Antti Karttunen

KEYWORD

allocated

STATUS

approved