A358174 Smaller of a pair of numbers (m, m+1) such that both are products P of composite prime powers with omega(P) > 1.
675, 9800, 235224, 465124, 1825200, 11309768, 384199200, 592192224, 4931691075, 5425069447, 13051463048, 221322261600, 865363202000, 8192480787000, 11968683934831, 13325427460800, 15061377048200, 28821995554247, 48689748233307, 511643454094368, 1558709801289000
Offset: 1
Keywords
Examples
a(1) = 675, since 675 = 3^3 * 5^2 and 676 = 2^2 * 13^2 are the smallest products of at least 2 composite prime powers that differ by 1. a(2) = 9800 since (3^4 * 11^2) - (2^3 * 5^2 * 7^2) = 1. a(3) = 235224 since (5^2 * 97^2) - (2^3 * 3^5 * 11^2) = 1.
Programs
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Mathematica
nn = 2^36; s = Select[Rest@ Union@ Flatten@ Table[a^2*b^3, {b, nn^(1/3)}, {a, Sqrt[nn/b^3]}], ! PrimePowerQ[#] &]; Map[s[[#]] &, Position[Differences[s], 1][[All, 1]] ]
Comments