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A331813
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a(n) is the least k > 1 such that k*A019278(n) belongs to A019278 too, or a(n) = 0 if no such k exists.
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0
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2, 2, 2, 2, 4, 4, 2, 7, 2, 4, 8, 2, 3, 2, 2, 4, 2, 64, 3, 64, 4, 8, 7, 4, 15, 3, 50, 2, 2, 50, 2, 7, 29184, 2, 16, 64, 4, 16, 4, 385, 15, 9, 313600, 2, 4, 2793, 4199, 2, 4, 57600
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OFFSET
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1,1
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COMMENTS
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For the 132 terms (< 5*10^11) of the b-file for A019278, and using an extended list of terms, it can be checked that a(n) is not 0, even if the precise value is not known. For instance, a(51) <= 8097830664651.
Then a(52) to a(82) are: 4, 9, 1197, 8, 256, 4, 65155475, 64, 4096, 16, 195205791, 1387, 7, 37791, 4, 119, 8, 35136, 225, 64, 69127695, 2129920, 256, 4, 19671223, 9, 2, 1379763, 8, 90, 4096. And a(83) <= 7758260899200.
a(51) and a(83) are > 10^9.
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LINKS
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EXAMPLE
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With A019278 starting as 1, 2, 4, 8, 15, 16, 21, 24, 42, 60, 64, ...
one gets the proper multiples 2, 4, 8, 16, 60, 64, ...
and so the sequence begins: 2, 2, 2, 2, 4, 4, ...
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PROG
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(PARI) a(n, v019278) = my(m = v019278[n]); my(k=2, y = k*m); while (denominator(sigma(sigma(y))/y) != 1, k++; y += m); k;
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CROSSREFS
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Cf. A019278 (integers m such that sigma(sigma(m))/m is an integer).
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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