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Search: id:A112265
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| A112265 |
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Cumulative sum of sum of initial digits of prime factors (with multiplicity) of n. |
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+0
3
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| 0, 2, 5, 9, 14, 20, 27, 33, 39, 46, 47, 54, 55, 64, 72, 80, 81, 90, 91, 100, 110, 113, 115, 124, 134, 137, 146, 157, 158, 168, 171, 181, 185, 188, 196, 206, 209, 212, 216, 227, 231, 243, 247, 252, 263, 267, 271, 282, 296, 308, 312, 317, 322, 333, 339, 352, 356
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Primes in this sequence are A112266. Coincidentally, a(n) includes these powers: a(7) - 27 = 3^3, a(14) = 64 = 2^6, a(17) = 81 = 3^4, a(20) = 100 = 10^2, a(42) = 243 = 3^5, a(69) = 441 = 21^2, a(77) = 512 = 2^9.
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FORMULA
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a(1) = 0, and given the prime factorization i = (p_1)^(e_1) * (p_2)^(e_2) * ... * (p_k)^(e_k) then a(n) = SUM{from i = 1 to n} A(112264(i) = SUM{from i = 1 to n} (e_1)*A000030(p_1) + (e_2)*A000030(p_2) + ... + (e_k)*A000030(p_l).
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CROSSREFS
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Cf. A000030, A000040, A001221, A001222, A112264, A112266-A112273.
Sequence in context: A110443 A130029 A132296 this_sequence A075543 A132315 A132336
Adjacent sequences: A112262 A112263 A112264 this_sequence A112266 A112267 A112268
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KEYWORD
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base,easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost2(AT)yahoo.com), Aug 30 2005
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