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Search: id:A115386
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| A115386 |
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a(1) = 1. For n >= 2, a(n) = sum of the two (not necessarily distinct) earlier terms, a(j) and a(k), which maximizes d(a(j)+a(k)), where d(m) is the number of positive divisors of m. a(n) = the maximum (a(j)+a(k)) if more than one such sum has the maximum number of divisors. |
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+0
2
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| 1, 2, 4, 8, 12, 24, 48, 96, 120, 240, 480, 720, 1440, 2880, 5760, 8640, 10080, 20160, 40320, 60480, 120960, 241920, 302400, 604800, 665280, 1330560, 2661120, 3326400, 6652800, 13305600, 26611200, 39916800, 43243200, 86486400, 172972800
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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In A115387 the minimum (a(j)+a(k)) is taken in case of a tie.
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LINKS
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Leroy Quet, Home Page (listed in lieu of email address)
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EXAMPLE
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Sequence begins 1, 1, 2, 4. Now d(1+1) = 2, d(1+2) = 2, d(1+4) = 2, d(2+2) = 3, d(2+4) = 4, d(4+4)=4. So d(2+4) and d(4+4) are tied for the maximum number of divisors of a sum of two earlier terms of the sequence. But we want the maximum sum among these two values. So a(5) = 4+4 = 8.
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PROGRAM
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(PARI) {print1(a=1, ", "); v=[a]; for(n=2, 35, dsmax=0; smax=0; for(j=1, #v, for(k=j, #v, s=v[j]+v[k]; d=numdiv(s); if(dsmax==d, smax=max(smax, s), if(dsmax<(d), dsmax=d; smax=s)))); print1(smax, ", "); v=concat(v, smax))}
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CROSSREFS
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Cf. A115387.
Sequence in context: A089821 A097942 A004653 this_sequence A058771 A036493 A082906
Adjacent sequences: A115383 A115384 A115385 this_sequence A115387 A115388 A115389
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KEYWORD
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nonn
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AUTHOR
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Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), following a suggestion of Leroy Quet Jan 22 2006
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