

A324111


Numbers n for which A324108(n) = A324054(n1) and which are neither prime powers nor of the form 2^i * p^j, where p is an odd prime, with either exponent i or j > 0.


7



1, 87, 174, 348, 696, 1392, 2091, 2784, 4182, 5568, 8364, 11136, 16683, 16728, 22272, 33215, 33366, 33456, 44544, 66430, 66732, 66912, 89088, 132860, 133464, 133824, 178176, 265720, 266928, 267179, 267648, 356352, 531440, 533856, 534358, 535296, 712704, 1062880, 1066877, 1067712, 1068716, 1070592, 1319235, 1425408
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OFFSET

1,2


COMMENTS

Setwise difference of A324109 and A070776.
Setwise difference of A070537 and A324110.
If an odd number n > 1 is present, then all 2^k * n are present also. Odd terms > 1 are given in A324112.


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..173


EXAMPLE

87 is a term, as 87 = 3*29, A324054(31) = 4, A324054(291) = 156, and A324108(87) = 4*156 = 624 = A324054(871).


PROG

(PARI)
A000265(n) = (n/2^valuation(n, 2));
A324054(n) = { my(p=2, mp=p*p, m=1); while(n, if(!(n%2), p=nextprime(1+p); mp = p*p, if(3==(n%4), mp *= p, m *= (mp1)/(p1))); n>>=1); (m); };
A324108(n) = { my(f=factor(n)); prod(i=1, #f~, A324054((f[i, 1]^f[i, 2])1)); };
isA324111(n) = ((1!=omega(n))&&(1!=omega(A000265(n)))&&(A324054(n1)==A324108(n)));
for(n=1, 2^20, if(isA324111(n), print1(n, ", ")))


CROSSREFS

Cf. A070537, A070776, A324109, A324110, A324112.
Sequence in context: A147140 A044257 A044638 * A044419 A044800 A067749
Adjacent sequences: A324108 A324109 A324110 * A324112 A324113 A324114


KEYWORD

nonn


AUTHOR

Antti Karttunen, Feb 15 2019


STATUS

approved



