

A324106


Multiplicative with a(p^e) = A005940(p^e).


12



1, 2, 3, 4, 5, 6, 9, 8, 7, 10, 15, 12, 25, 18, 15, 16, 11, 14, 21, 20, 27, 30, 45, 24, 49, 50, 75, 36, 125, 30, 81, 32, 45, 22, 45, 28, 55, 42, 75, 40, 77, 54, 105, 60, 35, 90, 135, 48, 121, 98, 33, 100, 245, 150, 75, 72, 63, 250, 375, 60, 625, 162, 63, 64, 125, 90, 39, 44, 135, 90, 99, 56, 91, 110, 147, 84, 135, 150, 189, 80, 143, 154, 231, 108, 55
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OFFSET

1,2


COMMENTS

Question: are there any other numbers n besides 1 and those in A070776, for which a(n) = A005940(n)? At least not below 2^25. This is probably easy to prove.


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384
Index entries for sequences related to binary expansion of n


EXAMPLE

For n = 85 = 5*17, a(85) = A005940(5) * A005940(17) = 5*11 = 55. Note that A005940(5) is obtained from the binary expansion of 51 = 4, which is "100", and A005940(17) is obtained from the binary expansion of 171 = 16, which is "1000".


PROG

(PARI)
A005940(n) = { my(p=2, t=1); n; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ From A005940
A324106(n) = { my(f=factor(n)); prod(i=1, #f~, A005940(f[i, 1]^f[i, 2])); };


CROSSREFS

Cf. A005940, A070776, A324107 (fixed points), A324108, A324109.
Sequence in context: A269387 A207801 A340364 * A252753 A005940 A332815
Adjacent sequences: A324103 A324104 A324105 * A324107 A324108 A324109


KEYWORD

nonn,mult


AUTHOR

Antti Karttunen, Feb 15 2019


STATUS

approved



