The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A332824 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A332824

a(n) = Product_{d|n} A019565(phi(d)), where phi is Euler totient function A000010.
(history; published version)

#7 by Susanna Cuyler at Tue Feb 25 18:33:55 EST 2020

STATUS

proposed

approved

#6 by Antti Karttunen at Tue Feb 25 16:40:58 EST 2020

STATUS

editing

proposed

#5 by Antti Karttunen at Tue Feb 25 16:40:38 EST 2020

NAME

a(n) = Product_{d|n} A019565(phi(d)), where phi is the Euler totient function A000010.

#4 by Antti Karttunen at Tue Feb 25 15:38:59 EST 2020

LINKS

Antti Karttunen, <a href="/A332824/b332824.txt">Table of n, a(n) for n = 1..8192</a>

CROSSREFS

Cf. A000010, A019565, A048675, A097248, A318834, A332825, A332826, A332827.

Cf. A048675 (a left inverse).

#3 by Antti Karttunen at Tue Feb 25 14:47:21 EST 2020

CROSSREFS

Cf. A000010, A019565, A048675, A097248, A318834, A332825, A332826, A332827.

#2 by Antti Karttunen at Tue Feb 25 14:25:28 EST 2020

NAME

allocated for Antti Karttunena(n) = Product_{d|n} A019565(phi(d)), where phi is the Euler totient function A000010.

DATA

2, 4, 6, 12, 10, 36, 30, 60, 90, 100, 42, 540, 70, 900, 210, 420, 22, 8100, 66, 2100, 3150, 1764, 330, 18900, 550, 4900, 2970, 94500, 770, 44100, 2310, 4620, 6930, 484, 11550, 4252500, 130, 4356, 16170, 115500, 182, 9922500, 546, 291060, 242550, 108900, 2730, 1455300, 8190, 302500, 858, 1131900, 1430, 8820900, 19110

OFFSET

1,1

FORMULA

a(n) = Product_{d|n} A332825(d).

a(n) = A318834(n) * A332825(n).

A048675(a(n)) = n.

A097248(a(n)) = A019565(n).

PROG

(PARI)

A019565(n) = {my(j, v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ From A019565

A332824(n) = { my(m=1); fordiv(n, d, m *= A019565(eulerphi(d))); (m); };

CROSSREFS

Cf. A000010, A019565, A048675, A097248, A318834, A332825.

KEYWORD

allocated

nonn

AUTHOR

Antti Karttunen, Feb 25 2020

STATUS

approved

editing

#1 by Antti Karttunen at Tue Feb 25 09:44:28 EST 2020

NAME

allocated for Antti Karttunen

KEYWORD

allocated

STATUS

approved