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A332445
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Numbers k of the form 4m+1 for which A087808(sigma(k)) is equal to 2*A087808(k).
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5
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2009, 19377, 37809, 59373, 74673, 115677, 270041, 310329, 354609, 357309, 720425, 732321, 841437, 2071737, 2612269, 3131149, 3866461, 3930929, 5172093, 5593981, 7118753, 7903961, 8224173, 9327393, 9438129, 11452321, 12708025, 18857209, 18861889, 18875313, 19110321, 20278269, 20709225, 20950061, 23963597, 24895153
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OFFSET
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1,1
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COMMENTS
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Numbers k such that A332224(k) is equal to A087808(2*k) and k == 1 mod 4.
Notably, the only square among the first 299 terms is a(248) = 5808421369 = 76213^2. sigma(5808421369) = 5808497583 == 3 (mod 4) == 7 (mod 8). Of the remaining 298 terms < 2^33, 92 are such that sigma(k) == 6 (mod 8) and 206 are such that sigma(k) == 2 (mod 8), that is, are terms of A332227.
Question: Why the terms come in clusters? Compare also the scatterplots of A087808 and A332224, and a similar sequence A332465.
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LINKS
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Antti Karttunen, Table of n, a(n) for n = 1..299; all terms <= 2^33
Index entries for sequences where any odd perfect numbers must occur
Index entries for sequences related to sigma(n)
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PROG
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(PARI)
A087808(n) = if(n<1, 0, if(n%2==0, 2*A087808(n/2), A087808((n-1)/2)+1));
isA332445(n) = ((1==(n%4))&&(2*A087808(n)==A087808(sigma(n))));
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CROSSREFS
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Intersection of A016813 and A332446.
Cf. also A228058, A332227, A332465.
Cf. A000203, A087808, A286357, A332224, A332225, A332458.
Sequence in context: A172807 A153822 A153779 * A162242 A249955 A020433
Adjacent sequences: A332442 A332443 A332444 * A332446 A332447 A332448
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KEYWORD
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nonn
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AUTHOR
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Antti Karttunen, Feb 14 2020
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STATUS
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approved
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