A370130 - OEIS

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A370130

a(n) = A369669(A276086(n)), where A369669 is the greatest common divisor of the first and second arithmetic derivative of n, and A276086 is the primorial base exp-function.

0, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 3, 1, 1, 16, 1, 5, 5, 5, 5, 5, 5, 100, 25, 25, 175, 25, 25, 1, 3, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 4, 17, 1, 1, 5, 5, 5, 5, 20, 5, 25, 25, 25, 25, 325, 25, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 11, 1, 4, 1, 1, 1, 1, 1, 5, 5, 320, 95, 5, 5, 25, 25, 25, 25, 100, 25, 7, 7, 112, 7, 7, 7, 7, 7, 7, 7, 28 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`0,9`
	LINKS	`Antti Karttunen, Table of n, a(n) for n = 0..16384` `Index entries for sequences related to primorial base`
	FORMULA	`a(n) = A369669(A276086(n)).` `a(n) = gcd(A327860(n), A370131(n)).` `For n >= 1, a(n) = A085731(A327860(n)).`
	PROG	`(PARI)` `A003415(n) = if(n<=1, 0, my(f=factor(n)); nsum(i=1, #f~, f[i, 2]/f[i, 1]));` `A369669(n) = { my(d=A003415(n)); gcd(d, A003415(d)); };` `A276086(n) = { my(m=1, p=2); while(n, m = (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };` `A370130(n) = A369669(A276086(n));`
	CROSSREFS	`Cf. A003415, A068346, A085731, A276086, A327860, A328242 (positions of 1's), A370131.` `Cf. A000012, A024451, A143293.` `Sequence in context: A046592 A369875 A334432 * A010326 A196879 A193349` `Adjacent sequences: A370127 A370128 A370129 * A370131 A370132 A370133`
	KEYWORD	`nonn,look`
	AUTHOR	`Antti Karttunen, Feb 10 2024`
	STATUS	`approved`

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Last modified August 29 13:55 EDT 2024. Contains 375517 sequences. (Running on oeis4.)