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A128301
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Indices of squares (of primes) in the semiprimes.
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3
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1, 3, 9, 17, 40, 56, 90, 114, 164, 253, 289, 404, 484, 533, 634, 783, 973, 1031, 1233, 1373, 1452, 1683, 1842, 2112, 2483, 2676, 2779, 2995, 3108, 3320, 4124, 4384, 4775, 4926, 5593, 5741, 6172, 6644, 6962, 7448, 7955, 8108, 8978, 9147, 9512, 9697, 10842
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| A001358(a(n)) = A001248(n) = A000040(n)^2.
Numbers n with property that tau(semiprime(n)) is not semiprime. [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Oct 15 2010]
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LINKS
| Zak Seidov, Table of n, a(n) for n = 1..1000
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EXAMPLE
| a(4) = 17 as 49 = 7^2 = prime(4)^2, the fourth square in the semiprimes, is the seventeenth semiprime.
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PROG
| (perl) -MMath::Pari=factorint, PARI -wle 'my $c = 0; my $s = PARI 1; while (1) { ++$s; my($sp, $si) = @{factorint($s)}; next if @$sp > 2; next if $si->[0] + (@$si > 1 ? $si->[1] : 0) != 2; ++$c; print "$s => $c" if @$sp == 1}' (from Hugo van der Sanden (hv(AT)crypt.org), Sep 25 2007)
(PARI) a(n)=my(s=0, i=0); n=prime(n)^2; forprime(p=2, sqrt(n), s+=primepi(n\p); i++); s - i * (i-1)/2
\\ Charles R Greathouse IV, Apr 21, 2011
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CROSSREFS
| Cf. A128302, A001358, A001248, A072000.
Sequence in context: A123325 A116688 A011755 * A176148 A206701 A176354
Adjacent sequences: A128298 A128299 A128300 * A128302 A128303 A128304
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KEYWORD
| nonn
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AUTHOR
| Rick L. Shepherd (rshepherd2(AT)hotmail.com), Feb 25 2007
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